If f(x) is an exponential function where f(−1)=8 and f(8.5)=87, then find the value of f(3), to the nearest hundredth.

Harlen Pritchard

Harlen Pritchard

Answered question

2020-10-18

If the exponential function f(x) has values of f(-1)=8 and f(8.5)=87, then find the value of f(3), to the nearest hundredth.

Answer & Explanation

un4t5o4v

un4t5o4v

Skilled2020-10-19Added 105 answers

The exponential function is:
fx=abx
Using f(1)=8,
8=ab-1
Using f(8.5)=87,
87=ab8.5 (2)
Solve for aa using (1) to obtain (3):
a=8b(3)
Substitute (3) to (2) and solve for bb:
87=8bb8.5
87=8b9.5
10.875=b9.5
10.87519.5=b
b1.2856
Solve for aa using (3):
a=810.87519.5
a10.2846
So, the exponential function is: fx=10.28461.2856x
For x=3.
f3=10.28461.28563
f(3)21.85

Jeffrey Jordon

Jeffrey Jordon

Expert2021-08-11Added 2605 answers

Answer is given below (on video)

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