Question

An initial investment of $60.00 increases in value by 15% each year. Which of the following statements are true? Select all that apply.

Select answers;
This function can be represented by the quadratic equation f(x)=0.15(x+60)^2
This situation can be represented by the exponential function f(x)=60 x 1.15^x
This function has no x-intercept
After 4 years the value of the investment will be $120.00
After 6 years the value of the investment will be $653.00
After 7.86 years the value of the investment will be 3 times the initial value
After 8 years the value of the investment will be $184.00

Answer 1

The situations can be represented by the exponential function f(x)=60x1.15^x
After 7.86 years the value of the investment will be three times the initial value (If you round to the nearest dollar)
After 8 years the value of the investment will be $184.00 (If you round to the nearest dollar)

Answer 2

Answer: The function can be represented by the exponential function :

$f(x)=60(1+0.15)^x=60(1.15)^x$

This function has no x-intercept .

After 7.86 years the value of the investment will be 3 times the initial value  .

After 8 years the value of the investment will be $184.00.

Step-by-step explanation:

The exponential growth function is given by :-

$f(x)=A(1+r)^x$, where A is the initial value , r is the rate of growth and x is the time period.

Given: A = $60

r=15%=0.15

Now, the function can be represented by the exponential function :

$f(x)=60(1+0.15)^x=60(1.15)^x$

We know that exponential function has no intercept , thus this function has no intercept.

∴

Now, at x=4

$f(4)=60(1.15)^4\approx104.94$

Now, at x=6

$f(6)=60(1.15)^6=138.78\approx139$

Now, at x=7.86

$f(7.86)=60(1.15)^{7.86}=179.98180=3(60)$

∴ After 7.86 years the value of the investment will be 3 times the initial value

Now, at x=8

$f(8)=60(1.15)^8=183.54\approx184$