If f(x) is an exponential function where f(2) = 29 and f(5) = 56, then the value of f(10) = 173.13
The f(x) is an exponential function
The general form of exponential function is
f(x) = [tex]ab^x[/tex]
The value of f(2) = 29
Then,
29 = [tex]ab^2[/tex]
The value of f(5) = 56
The equation will be
56 = [tex]ab^5[/tex]
Divide the second equation by first equation
[tex]ab^5[/tex] / [tex]ab^2[/tex] = 56 /29
[tex]b^3[/tex] = 56/29
b = 1.25
Substitute the value of b in the first equation
29 = [tex]ab^2[/tex]
a × [tex](1.25)^2[/tex] = 29
a × 1.56 = 29
a = 29/1.56
a = 18.59
Then the value of f(10) = (18.59) × [tex]1.25^{10}[/tex]
= 173.13
Hence, if f(x) is an exponential function where f(2) = 29 and f(5) = 56, then the value of f(10) = 173.13
Learn more about exponential function here
brainly.com/question/11487261
#SPJ4
