kassidymorrisp
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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?​

Respuesta :

mixter17

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:

[tex]P(t)=StartAmount*(rate)^{t}[/tex]

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:

[tex]f(x)=250(1.03)^{x}[/tex]

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:

[tex]Rate=1+percent(growth)[/tex]

- 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!

The exponent represents

  • The x can never be negative so it is growing.
  • The base is 1.03, then the rate will be 1.03.
  • 250 represents the principal value that was invested initially.

What is an exponent?

An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.

Given

The exponential function [tex]\rm f(x)=250(1.03)^x[/tex]

where x is the number of years.

Part A: The money in the account growing or decaying.

If the power increases the value of the function increases.Since the x can never be negative so it is growing.

Part B: The rate of growth or decay.

The rate of growth is the base of the exponent.

Since the base is 1.03, then the rate will be 1.03.

Part C: The value 250 represents.

250 represents the principal value that was invested initially.

A. The x can never be negative so it is growing.

B. The base is 1.03, then the rate will be 1.03.

C. 250 represents the principal value that was invested initially.

More about the exponent link is given below.

https://brainly.com/question/5497425

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