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

Answer:

$40,000

Step-by-step 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

Answer 2

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.