Question

This equation represents an exponential function that passes through the point (2, 80).

Answer 1

we know that

If the point belongs to the graph, then the point must satisfy the equation

we will proceed to verify each case

case A.) $f(x)=4(x^{5})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=4(2^{5})$

$f(2)=128$

$128\neq 80$

therefore

the equation $f(x)=4(x^{5})$ not passes through the point $(2,80)$

case B.) $f(x)=5(x^{4})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=5(2^{4})$

$f(2)=80$

$80=80$

therefore

the equation $f(x)=5(x^{4})$ passes through the point $(2,80)$

case C.) $f(x)=4(5^{x})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=4(5^{2})$

$f(2)=100$

$100\neq 80$

therefore

the equation $f(x)=4(5^{x})$ not passes through the point $(2,80)$

case D.) $f(x)=5(4^{x})$

The point is $(2,80)$

Verify if the point satisfy the equation

For $x=2$ find the value of y in the equation and compare with the y-coordinate of the point

$f(2)=5(4^{2})$

$f(2)=80$

$80=80$

therefore

the equation $f(x)=5(4^{x})$  passes through the point $(2,80)$

therefore

the answer is

$f(x)=5(x^{4})$

$f(x)=5(4^{x})$

Answer 2

"f(x) = 5(4)x" is the one equation among the following choices given in the question that represents an exponential function that passes through the point (2, 80). The correct option among all the options that are given in the question is the fourth option or option "D". I hope that the answer has come to your help.