Question

Samuel took an antique clock that his grandfather had purchased, to be appraised. The appraiser evaluated the current price of the clock to be $400 and stated that the value will continue to increase at 2% per year.

Which of the following graphs shows the value of the antique clock, y, in dollars, after x years?

Answer 1

I'm pretty sure to find the number to multiply 400 by, it is 1.02^x, x being the number of years. So, do that with 20, then multiple the number by 400, so it should be the 1st one.

Answer 2

The correct option is 1.

Explanation:

The general exponential function is

`y=a(1+r)^x`

Where, a is the initial value, r is rate of change and x is number of years.

It is given that the appraiser evaluated the current price of the clock to be $400 and stated that the value will continue to increase at 2% per year.

It means

`a=400`

`r=2\%=0.02`

The price of the clock after x years is

`y=400(1+0.02)^x`

`y=400(1.02)^x`

At x=0,

`y=400(1.02)^(0)=1`

At x=20,

`y=400(1.02)^((20))=594.38`

At x=40,

`y=400(1.02)^((40))=883.22`

It means the graph of the function passes through points (0,400), (20,594.38) and (40,883.22).

Therefore the correct option is 1.