Christopher deposited 1 billion into his savings. His savings is a compound interest account with a rate of 9% and only compound once a year. How much money would Christopher have at the end of 10 years in millions?

P'=2,367 million $

Step-by-step explanation:

Compound Interest

It refers to the case where the interests earned in a certain period are added to the principal sum of a loan and re-invested. Interest in the next period is then earned on the principal sum plus previously accumulated interest.

Being P the principal, or initial amount of a loan or deposit, r the nominal annuual interest rate and t the time the interest is applied, the total accumlated value or future value is

According to the conditions of the problem, Christopher deposited 1 billion into his savings. This gives us the principal P=1,000 milion dollars. The interest rate is 9% compounded once a year during t=10 years. Here n=1 since the compounding does not occur in the middle of the yearly period. Thus

The path of the football is an illustration of parabolas.

The function is given as:

(a) The maximum height

First, we differentiate the function with respect to x

Set the above equation to 0

Collect like terms

Divide both sides by -0.06

Substitute 25.5 for x in

Hence, the maximum height is:

(b) How far the football is kicked

Equate to 0

Now, we solve for x (i.e. the horizontal distance)

Divide both sides by -x

Divide both sides by 0.03

Hence, the football is kicked to 51 yards

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