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?

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.

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DelcieRiveria DelcieRiveria · Answer 2 · 2019-05-22T11:16:23+02:00

Answer:

The correct option is 1.

Step-by-step explanation:

The general exponential function is

[tex]y=a(1+r)^x[/tex]

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

[tex]a=400[/tex]

[tex]r=2\%=0.02[/tex]

The price of the clock after x years is

[tex]y=400(1+0.02)^x[/tex]

[tex]y=400(1.02)^x[/tex]

At x=0,

[tex]y=400(1.02)^(0)=1[/tex]

At x=20,

[tex]y=400(1.02)^{(20)}=594.38[/tex]

At x=40,

[tex]y=400(1.02)^{(40)}=883.22[/tex]

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.