Question

40 POINTS, ANY GUESSES WILL BE REPORTED!!

Function f is an exponential function. It predicts the value of a trading card, in hundreds of dollars, as a function of the number of decades since it was last purchased.

What equation models this function?

Answer 1

the correct answer is 4(1.75)x :)

Answer 2

Answer:
`y=4(1.75)^x`

Explanation:

Given graph models a function f which is an exponential function.

We know that the exponential function is given by

`y=Ab^x`, b is the rate of change and x is the time period.

In the given graph we see two points as (0,4) and (1,7)

Now, put x=0 and y=4 (for first point) in the exponential function such that

`4=Ab^0\\\Rightarrow4=A\ or\ A=4`

Put x=1, y=7 and A=4 (for second point) in the exponential function such that

`7=4b^1\\\Rightarrow7=4b\\\Rightarrow\ b=(7)/(4)\\\Rightarrow\ b=1.75`

Now substitute A=4 and b=1.75 in the standard exponential function we get our equation that models the given function that predicts the value of a trading card, in hundreds of dollars (y)

`y=4(1.75)^x`, where x is the number of decades.