Answer:
[tex]f(x)=10\cdot (5^2)^{\frac{x}{2}}[/tex]
Step-by-step explanation:
We have been given a function [tex]f(x)=10\cdot 5^x[/tex], which represents represents the growth of a lizard population every year in a remote desert.
As Christa wants to write an an equivalent form that calculates every half-year, so we need to manipulate our function in such a way that when we substitute x = 1, the outer exponent becomes half.
That would be only possible, if we had x/2 in the outer exponent.
Using exponent property we can [tex]a^{b*c}=(a^b)^c[/tex] we can write a function that calculates the lizard population every half-year as:
[tex]10\cdot (5)^x=10\cdot (5^2)^{\frac{x}{2}}[/tex]
Therefore, the function [tex]10\cdot (5^2)^{\frac{x}{2}}[/tex] represents the growth of lizard population every half year.
