Question

HELP PLEASE!

Function f is an exponential function. It predicts the value of a famous sculpture, in thousands of dollars, as a function of the number of years since it was last purchased.

What equation models this function?

Answer 1

Answer: y = 5*(7/5)^x
Note: In decimal form, the equation is y = 5*(1.4)^x because 7/5 = 1.4

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Step-by-step explanation:

The general exponential form is y = a*b^x
Plug in the first point (x,y) = (0,5) and we can find 'a' to be...
y = a*b^x
5 = a*b^0
5 = a*1
5 = a
a = 5

Which means y = a*b^x updates to y = 5*b^x
Now plug in the other point (x,y) = (1,7) to find b
y = 5*b^x
7 = 5*b^1
7 = 5*b
b = 7/5
b = 1.4

So the equation is y = 5*(7/5)^x which is equivalent to y = 5*(1.4)^x