Question

The amount of money in an investment is modeled by the function A(t)=650(0.943)t. The variable A represents the investment balance in dollars, and t the number of years since 2006.

(A) In 2006, the balance was $.

(B) The amount of money in the investment is

(C) The annual rate of change in the balance is
r= or r=%.

(D) In the year 2016 the investment balance will equal
$. Round answer to the nearest penny.

Answer 1

According to the question , the amount of money in an investment is modeled by the function of

Where the variable represents the investment balance in dollars, and t the number of years since 2006.

(A) In 2006, the balance was $

Explanation:

In 2006, the t value is , we replace this at the function we get:

(B) The amount of money in the investment is $.

Explanation:

As this function shows the investment from 2006 and at initial year total amount is equal to the initial investment due to power of the interest rate function is zero of growth rate of money.

(C) The annual rate of change in the balance is determined as   %.

Explanation:

Let us initial investment at 2006 as:

Balance after one year 2007 is determined as:

Therefore the change in balance in one year is:

Therefore the percentage change is determined as:

With negative sign as the balance decreases over the year.

(D) In the year 2016 the investment balance will equal  .

Explanation:

In 2016, the t value is calculated as years.

Round answer to the nearest penny.