Question

A limited-edition poster increases in value each year. After 1 year, the poster is worth $20.70. After 2 years, it is worth $23.81. Which equation can be used to find the value, y, after x years? (Round money values to the nearest penny.)

y = 18(1.15)x
y = 18(0.15)x
y = 20.7(1.15)x
y = 20.7(0.15)x

Answer 1

This is an exponential function represented by

$y=a(b)^{x}$

When x = 1, y= 20.7

when x = 2 , y = 23.81

Substituting the values we get

$20.7=ab$

$23.81=ab^2$

Dividing second equation by the first we get

$\frac{23.81}{20.7}=\frac{ab^2}{ab}$

We get b =1.15

Substituting the value of b in the first equation we get

$20.7=a(1.15)$

We get a = 18

Our equation becomes

$y=18(1.15)^x$

Option A) or the first option is the right answer.