Answer:
[tex]f(x)=10(5^{2})^{\frac{x}{2}}[/tex] (first option)
Step-by-step explanation:
we have
[tex]f(x)=10(5)^{x}[/tex]
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
[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]
