Question

Samantha is considering investing $1,000 in a savings account that earns 3.55% interest and compounds annually. Which of the following function rules would appropriately model Samantha’s investment? a. f(x) = 3.55x + 1000 b. f(x) = 3.55(1000)x c. f(x) = 1000(.0355)x d. f(x) = 1000(1 + .0355)x

Answer 1

Option d.
`f(x)=\$1,000(1+0.0355)^(x)`

Explanation:

we know that

The compound interest formula is equal to

`A=P(1+(r)/(n))^(nt)`

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest in decimal

t is Number of Time Periods

n is the number of times interest is compounded per year

in this problem we have

`t=x\ years\\ P=\$1,000\\ r=0.0355\\n=1`

substitute in the formula above

`A=\$1,000(1+(0.0355)/(1))^(1*x)`

`A=\$1,000(1+0.0355)^(x)`

Convert to function notation

`f(x)=\$1,000(1+0.0355)^(x)`