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Sagot :
Using an exponential function, it is found that the value of the function when x = 4 is of f(4) = 15.95.
What is an exponential function?
It is modeled by:
[tex]y = ab^x[/tex]
In which:
- a is the initial value.
- b is the rate of change, as a decimal.
In this problem, we have that f(-1)=5, hence:
[tex]5 = ab^{-1}[/tex]
[tex]\frac{a}{b} = 5[/tex]
a = 5b
We also have that f(7)=32, hence:
[tex]32 = ab^7[/tex]
Since a = 5b:
[tex]5b^8 = 32[/tex]
[tex]b = \sqrt[8]{\frac{32}{5}}[/tex]
b = 1.2612.
a = 5b = 5 x 1.2612 = 6.306.
Hence the function is given by:
[tex]y = 6.306(1.2612)^x[/tex]
Then, when x = 4, we have that:
[tex]y = 6.306(1.2612)^4 = 15.95[/tex]
More can be learned about exponential functions at https://brainly.com/question/25537936
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