Answer:
![f(x)=10\cdot (5^2)^{\frac{x}{2}}](https://tex.z-dn.net/?f=f%28x%29%3D10%5Ccdot%20%285%5E2%29%5E%7B%5Cfrac%7Bx%7D%7B2%7D%7D)
Step-by-step explanation:
We have been given a function
, 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
we can write a function that calculates the lizard population every half-year as:
Therefore, the function
represents the growth of lizard population every half year.