Question

Consider the exponential function f(x)=250(1.03)^x which models Shawnda's savings account where x represents the number of years since the money was invested
part a: is the money in the account growing or decaying?

part b: what is the rate of growth or decay?

part c: what does the value 250 represent?​

Answer 1

Hello!

The answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

Why?

To solve the problem, first, we must remember the structure of the exponential growth or decay function:

$P(t)=StartAmount*(rate)^{t}$

Where,

- Start Amount, is the starting value or amount

- Rate, is the rate of growth or decay, we must consider the following conditions:

If the rate is greater than 1, the rate is a growth rate.

If the rate is lower than 1, the rate is a decay rate.

- t, is the time elapsed.

Therefore, we are given the following function:

$f(x)=250(1.03)^{x}$

From the function we can see that:

- Since the rate is 1.03 and it's greater than 1, the money in the account is growing.

- From the function we already know that the rate of growth is equal to 1.03

The rate is calculated by the following formula:

$Rate=1+percent(growth)$

- The value 250 represents the starting amount of money.

Hence, the answers are:

Part a: The money in the account is growing.

Part b: The rate of growth is 3%

Part c: The value 250 represents the starting amount of money.

Have a nice day!