Oliver invested $970 in an account paying an interest rate of 7 1/2 % compounded continuously. Carson invested $970 in an account paying an interest rate of 7 3/8% compounded annually. To the nearest of a hundredth of a year, how much longer would it take for Carson's money to double than for Oliver's money to double?

0.50 or about half a year longer.

Step-by-step explanation:

We can write an equation to model bot investments.

Oliver invested $970 in an account paying an interest rate of 7.5% compounded continuously.

Recall that continuous compound is given by the equation:

Where A is the amount afterwards, P is the principal amount, r is the rate, and t is the time in years.

Since the initial investment is $970 at a rate of 7.5%:

Carson invested $970 in an account paying an interest rate of 7.375% compounded annually.

Recall that compound interest is given by the equation:

Where A is the amount afterwards, P is the principal amount, r is the rate, n is the number of times compounded per year, and t is the time in years.

Since the initial investment is $970 at a rate of 7.375% compounded annually:

When Oliver's money doubles, he will have $1,940 afterwards. Hence:

Solve for t:

Take the natural log of both sides:

Simplify:

When Carson's money doubles, he will have $1,940 afterwards. Hence:

Solve for t:

Take the natural log of both sides:

Simplify:

Hence:

Then it will take Carson's money:

About 0.50 or half a year longer to double than Oliver's money.

just take the area of the square and then the area of the circle then subtract the circle area from the squares area

step-by-step explanation: