Answer:
\(f(x)=10\cdot (5^2)^{\frac{x}{2}}\)
Step-by-step explanation:
We have been given a function \(f(x)=10\cdot 5^x\), 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 \(a^{b*c}=(a^b)^c\) we can write a function that calculates the lizard population every half-year as:
\(10\cdot (5)^x=10\cdot (5^2)^{\frac{x}{2}}\)
Therefore, the function \(10\cdot (5^2)^{\frac{x}{2}}\) represents the growth of lizard population every half year.
