Recall that the equation for compounded interest (with annual compounding) is:

Where  is the balance,  is the rate of interest, and  is the number of years.

Thus, for our data, we need to know:

This is approximately .

Recall that the equation for compounded interest (with quarterly compounding) is:

Where  is the balance,  is the rate of interest,  is the number of years, and  is the number of times it is compounded per year.

Thus, for our data, we need to know:

This is approximately .

Recall that the equation for compounded interest (with annual compounding) is:

Where  is the balance,  is the rate of interest, and  is the number of years.

Thus, for our data, we need to know:

Now, let's use  for . This gives us:

Using a logarithm, this can be rewritten:

This can be rewritten:

Now, you can solve for :

or

Now, finally you can rewrite this as:

Thus, 

Now, round this to  and recall that 

Thus,  and  or 

First, break the problem into two segments: the amount Jack invests in the high-yield savings, and the amount Jack invests in the simple interest account (10,000 and 5,000 respectively).

Now let's work with the high-yield savings account. $10,000 is invested at an annual rate of 8%, compounded quarterly. We can use the compound interest formula to solve:

Plug in the values given:

Therefore, Jack makes $824.32 off his high-yield savings account. Now let's calculate the other interest:

Add the two together, and we see that Jack makes a total of,  off of his investments.

The formula to use for compounded interest is  

where P is the principal (original) amount, r is the interest rate (expressed in decimal form), n is the number of times per year the interest compounds, and t is the total number of years the money is left in the bank. In this problem, P=1,500, r=0.042, n=12, and t=3.

By plugging in, we find that Michelle will have about $1,701 at the end of three years.

In order to transform a negative integer to a positive one, it must be taken to an even power, and to make it a fraction between 0 and 1, it must be taken to a negative power. The only choice that fits both criteria is -2. 

We can represent this as an exponential equation (just use million as a label and not a variable):

$1m * (1.15)⁵ = $2.01m

First, calculate the value of m by taking the two-thirds root of both m^3/2 and 64, leaving m=16. Then solve the expression by plugging in 16 for m. This gives 16² + 3(16) = 256 + 48 = 304.

We know that the expression must be negative. Therefore one or all of the terms x⁷, y⁸ and z¹⁰ must be negative; however, even powers always produce positive numbers, so y⁸ and z¹⁰ will both be positive. Odd powers can produce both negative and positive numbers, depending on whether the base term is negative or positive. In this case, x⁷ must be negative, so x must be negative. Thus, the answer is x < 0.