This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

Step 2: Calculate .

Step 3: Substitute in known values into the half life formula to solve for .

This question is testing one's ability to recognize real life situations that have a exponential growth or decay over a certain interval and how to deal with them in function form.

For the purpose of Common Core Standards, recognize situations that have a exponential growth or decay over a certain interval, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.A).

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify the known values given in the question.

Step 2: Calculate .

Step 3: Substitute in known values into the half life formula to solve for .

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The red lines in the below graph represent the slope.

The rise is three units up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The red lines in the below graph represent the slope.

The rise is two units up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is one unit up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is three units up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is two units up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is four units up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is one unit up and the run is two units to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2). 

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

The rise is one unit up and the run is one unit to the right.

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

.

Substitute the slope and intercept into the general form to construct this particular function.