Question

the function f(x) = 3,005(1+0.03)^x represents the amount of money in a savings account where x represents time in years. what does 3,005 represent? a. the amount of money in the savings account after one year b. the amount of money added to the savings account each year c. the growth rate d. the initial amount of money placed in the savings account

Answer 1

d. The initial amount of money placed in the savings account

Explanation:

Given function that represents the amount of money after x years,

`f(x)=3005(1+0.03)^x`

Which is an exponential growth function,

Since, in a growth function,

`f(x)=ab^x`

a represents the initial value,

b is the growth rate per period,

x is the number of periods,

By comparing,

a = 3005,

Hence, 3005 must be represent the initial amount of money placed in the savings account,

Option 'd' is correct.

Answer 2

Option d. the initial amount of money placed in the savings account

Explanation:

we have

`f(x)=3,005(1+0.03)^(x)`

This is a exponential function of the form

`f(x)=a(1+r)^(x)`

where

a is the initial value

r is the growth rate

(1+r) is the base

x is the number of years

f(x) is the amount of money in a savings account

In this problem we have

a=$3,005

r=0.03=3%

(1+r)=1.03

therefore

3,005 represent the initial value ( the amount of money for the value of x equal to zero)