Question

which equation represents an exponential function that passes through the point (2, 80)? f(x) = 4(x)5 f(x) = 5(x)4 f(x) = 4(5)x f(x) = 5(4)x

Answer 1

we know that

if the exponential function passes through the given point, then the point must satisfy the equation of the exponential function

we proceed to verify each case  if the point $(2,80)$ satisfied the exponential function

case A  $f(x)=4(x^{5})$

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

so

$f(2)=4(2^{5})=128$

$128\neq 80$

therefore

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

case B  $f(x)=5(x^{4})$

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

so

$f(2)=5(2^{4})=80$

$80=80$

therefore

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

case C  $f(x)=4(5^{x})$

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

so

$f(2)=4(5^{2})=100$

$100\neq 80$

therefore

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

case D  $f(x)=5(4^{x})$

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

so

$f(2)=5(4^{2})=80$

$80=80$

therefore

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

therefore

the answer is

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

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