Question

An investment of $5000 doubles in value every decade. The function f(x) = 5000 · 2^x, where x is the number of decades, models the growth of the value of their investment. How much is the investment worth after 30 yr?

Answer 1

1 decade = 10 years
30 years = 3 decades

Simply plug in the value of the number of decades needed to find into where the x value is.
f(x) = 5000 · 2^x
f(3) = 5000 · 2^3 = 40000
The investment is worth $40000 after 30 years.

Answer 2

$40,000

Explanation:

We can see a Geometric Sequence if you pay attention to the Range.

Where
`a_(n) =5000*2^(n-1) \\ a_(1) =5000*2^0 =5000\\ a_(2) =5000*2^1=10,000\\ a_(3) =5000*2^2=20,000\\ a_(4)=5000*2^3=40,000\\`

{5000,10000,20000,40000,...}

x (Domain) | y (Range)

0 | 5,000

1 | 10,000

2 | 20,000

3 | 40,000

So in this function, 1 decade =10 years, by the end of 3 decades

y= US$40,000