Question

The function f(x) = 10(5)x represents the growth of a lizard population every year in a remote desert. Crista wants to manipulate the formula to an equivalent form that calculates every half-year, not every year. Which function is correct for Crista's purposes? (1 point)

f(x) = 10(52) the x over 2 power

f(x) = ten halves (5)x

f(x) = 10(5)x

f(x) = 10( 5 to the one half power )2x

Answer 1

`f(x)=10(5^(2))^{(x)/(2)}` (first option)

Explanation:

we have

`f(x)=10(5)^(x)`

where

x ----> is the time in years

we know that

Crista wants to manipulate the formula to an equivalent form that calculates every half-year

The exponent will be

x/2 -----> the time every half year

To find an equivalent form

`f(x)=10(5^(a))^{(x)/(2)}`

`10(5)^(x)=10(5^(a))^{(x)/(2)}`

`10(5)^(x)=10(5)^{a(x)/(2)}`

so

`x={a(x)/(2)}`

`a=2`

The equivalent form is

`f(x)=10(5^(2))^{(x)/(2)}`