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

An exponential function is always of the form $y=ab^x$ where a and b are constants.

Now, our case it has to be either $f(x) = 4(5)^x$ or $f(x) = 5(4)^x$ because the other two functions do not meet the basic requirement of the form of an exponential function.

Let us now check the point that has been given to us. It is (2,80). By trial and error we can easily see that the second function,  $f(x) = 5(4)^x$, passes through the point because if we plug in x=2, we get the value of y to be:

$y=5(4)^2=5\times 16=80$.

Thus, the equation $f(x) = 5(4)^x$ represents an exponential function that passes through the point (2, 80).

Answer 2

An exponential function is always of the form y = ab^x where a and b are constants.

Now, our case it has to be f(x) = 5(4) ^x because the other two functions do not meet the basic requirement of the form of an exponential function.

Given is (2, 80). By trial and error we can easily see that the second function, f(x) = 5(4) ^x , passes through the point because if we plug in x=2, we get the value of y to be:

f(x) = 5(4) ^x = 80

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