Q:

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 powerf(x) = ten halves (5)xf(x) = 10(5)xf(x) = 10( 5 to the one half power )2x

Accepted Solution

A:
Answer:[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex] Β (first option)Step-by-step explanation:we have[tex]f(x)=10(5)^{x}[/tex]wherex ----> is the time in yearswe know thatCrista wants to manipulate the formula to an equivalent form that calculates every half-yearThe exponent will bex/2 -----> the time every half yearTo find an equivalent form[tex]f(x)=10(5^{a})^{\frac{x}{2}}[/tex][tex]10(5)^{x}=10(5^{a})^{\frac{x}{2}}[/tex][tex]10(5)^{x}=10(5)^{a\frac{x}{2}}[/tex]so[tex]x={a\frac{x}{2}}[/tex][tex]a=2[/tex]The equivalent form is[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex]