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GRE Subject Test: Math : Exponential Functions

Study concepts, example questions & explanations for GRE Subject Test: Math

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2 Diagnostic Tests 148 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #901 : Rate

The rate of growth of the bacteria in an agar dish is proportional to the population. The population increased by 150 percent between 1:15 and 2:30. What is the constant of proportionality?

Possible Answers:

0.008

0.102

0.005

0.012

0.039

Correct answer:

0.012

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 150 percent between 1:15 and 2:30, we can solve for this constant of proportionality:

$(1+1.50)y_0=y_0e^{k(2:30 - 1:15)}$

Dealing in minutes:

$2.50=e^{75k}$

75k=ln(2.50)

$k=\frac{ln(2.50)}{75}=0.012$

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Example Question #12 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the duck population in Wingfield is proportional to the population. The population increased by 15 percent between 2001 and 2008. What is the constant of proportionality?

Possible Answers:

0.01997

0.31056

0.02961

0.00341

Correct answer:

0.01997

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 15 percent between 2001 and 2008, we can solve for this constant of proportionality:

$(1+.15)y_0=y_0e^{k(2008-2001)}$

$1.15=e^{7k}$

7k=ln(1.15)

$k=\frac{ln(1.15)}{7}=0.01997$

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Example Question #13 : How To Find Constant Of Proportionality Of Rate

The rate of decrease of the panda population is proportional to the population. The population decreased by 12 percent between 1990 and 2001. What is the constant of proportionality?

Possible Answers:

-2.526

-0.012

-0.034

-0.191

-0.891

Correct answer:

-0.012

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population decreased by 12 percent between 1990 and 2001, we can solve for this constant of proportionality:

$(1-0.12)y_0=y_0e^{k(2001-1990)}$

$0.88=e^{11k}$

11k=ln(0.88)

$k=\frac{ln(0.88)}{11}=-0.012$

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Example Question #2 : Exponential Growth Applications

The rate of growth of the salmon population of Yuba is proportional to the population. The population increased by 21 percent over the course of seven years. What is the constant of proportionality?

Possible Answers:

0.030

-1.755

0.027

0.133

0.289

Correct answer:

0.027

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 21 percent over the course of seven years, we can solve for this constant of proportionality:

$(1+0.21)y_0=y_0e^{7k}$

$1.21=e^{7k}$

7k=ln(1.21)

$k=\frac{ln(1.21)}{7}=0.027$

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Example Question #11 : Exponential Growth Applications

The rate of decrease of the number of concert attendees to former teen heartthrob Justice Beaver is proportional to the population. The population decreased by 34 percent between 2013 and 2015. What is the constant of proportionality?

Possible Answers:

-1.11

-0.21

0.15

-0.08

-0.40

Correct answer:

-0.21

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population decreased by 34 percent between 2013 and 2015, we can solve for this constant of proportionality:

$(1-0.34)y_0=y_0e^{k(2015-2013)}$

$0.66=e^{2k}$

2k=ln(0.66)

$k=\frac{ln(0.66)}{2}=-0.21$

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Example Question #16 : How To Find Constant Of Proportionality Of Rate

The rate of growth of the Land of Battlecraft players is proportional to the population. The population increased by 72 percent between February and October of 2015. What is the constant of proportionality?

Possible Answers:

0.093

0.068

0.012

0.118

0.059

Correct answer:

0.068

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population increased by 72 percent between February and October, we can solve for this constant of proportionality. It'll help to represent the months by their number in the year:

$(1+0.72)y_0=y_0e^{k(10-2)}$

$1.72=e^{8k}$

8k=ln(1.72)

$k=\frac{ln(1.72)}{8}=0.068$

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Example Question #911 : Rate

The rate of decrease of the gluten-eating demographic of the US is proportional to the population. The population decreased by 8 percent between 2014 and 2015. What is the constant of proportionality?

Possible Answers:

-0.194

-0.083

-0.109

-0.097

-0.177

Correct answer:

-0.083

Explanation:

We're told that the rate of growth of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

$p(t)=p_0e^{kt}$

Where p_0 is an initial population value, and is the constant of proportionality.

Since the population decreased by 8 percent between 2014 and 2015, we can solve for this constant of proportionality:

$(1-0.08)y_0=y_0e^{k(2015-2014)}$

$0.92=e^{k}$

k=ln(0.92)

k=-0.083

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Example Question #31 : Exponential Functions

Bob invests $\$10,000$ in a bank that compounds interest continuously at a rate of $12\%$ . How much money will Bob have in his account after years? (Round answer to decimal places.)

Possible Answers:

$\$14,333$

$\$15,000$

$\$14,000$

$\$14,333.29$

Correct answer:

$\$14,333.29$

Explanation:

Step 1: Recall the formula for continuously compounded interest

The formula is: $A=Pe^{rt}$ , where:

is the Final balance after years.

is the original investment balance.

is the exponential function

is the interest rate, usually written as a decimal

is the time, usually in years

Step 2: Plug in all the information that we have into the formula

$r=12\%=0.12$

$A=(\$10,000)e^{0.12(3)}$

Simplify:

$A=(\$10,000)e^{.36}$

Step 3: Evaluate.

$e^{.36}\approx1.433329$

$(\$10,000)(1.433329)=\$14,333.29$

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GRE Subject Test: Math : Exponential Functions

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #901 : Rate

Example Question #12 : How To Find Constant Of Proportionality Of Rate

Example Question #13 : How To Find Constant Of Proportionality Of Rate

Example Question #2 : Exponential Growth Applications

Example Question #11 : Exponential Growth Applications

Example Question #16 : How To Find Constant Of Proportionality Of Rate

Example Question #911 : Rate

Example Question #31 : Exponential Functions

All GRE Subject Test: Math Resources

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