Question

The value of a collector’s item is expected to increase exponentially each year. The item is purchased for $500. After 2 years, the item is worth $551.25. Which equation represents y, the value of the item after x years?

y = 500(0.05)x

y = 500(1.05)x

y = 500(0.1025)x

y = 500(1.1025

Answer 1

y = 500(1.05)x is the answer

551.25=500(1+r)^2
Solve for r
r=(551.25÷500)^(1÷2)−1
r=0.05

Answer 2

Answer:
`y=500(1.05)^x`

Explanation:

Given: The value of a collector’s item is expected to increase exponentially each year.

The exponential growth equation is given by :

`y=A(b)^x`, where A is the initial cost , b is the growth factor per year and x is the number of years.

The cost of item A= $500

After 2 years, the item is worth $551.25 (y), then we have the following equation

`551.25=500(b^2\\\\\Rightarrow\ (b)^2=(551.25)/(500)\\\\\Rightarrow\ (b)^2=1.1025\\\\\Rightarrow\ b=1.05`

When we substitute the values of A and b in the standard equation, we get equation represents y, the value of the item after x years will be:

`y=500(1.05)^x`