Question

Which of the following options is an equivalent function to f(x) = 2(5)^2x? choices: f(x) = 50^x f(x) = 100^x f(x) = 2(25)^x f(x) = 4(25)^x

Answer 1

For this case we have the following function:

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

By power properties we can rewrite the function as follows:

$f (x) = 2 ((5) ^ 2) ^ x$

We have then:

$(5) ^ 2 = 25$

Then rewriting the function we have:

$f (x) = 2 (25) ^ x$

Answer:

an equivalent function to $f (x) = 2 (5) ^ {2x}$ is:

$f (x) = 2 (25) ^ x$

Answer 2

F(X) = 2(5)^2x two times five equals 10. 10 to the power of two equals 100 because it's ten times ten. So F(X) = 100^x because that means it's just 100. Also F(x) = 4(25)^x because four times 25 equals 100.