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)x

Answer 1

i think it is C!!!!!!!!!!

Answer 2

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

Step-by-step explanation:

We know that the general exponential equation to find the value after x years is written as :-

$y=Ab^x$, where A is the initial value and b is the multiplicative rate of change and x is the time period.

Given : The initial amount of a product = $500

After 2 years, the item is worth $551.25.

Substitute A = 500, x=2 and y= 551.25 in the above equation we get

$551.25=500b^2\\\\\Rightarrow\ b^2=\dfrac{551.25}{500}\\\\\Rightarrow\ b^2=1.1025\\\\\Rightarrow\ b=\sqrt{1.1025}=1.05$

Now, substitute b= 1.05, A = 500 in the general exponential equation, we get the equation represents y, the value of the item after x years as :-

$y=500(1.05)^x$