Start by writing $f(2x-3)$ using $f(x)=250(5)^x$. Wherever $x$ appears in $f(x)$, replace it with $2x-3$.

After substitution, you will have a power like $5^{2x-3}$. Use rules such as $a^{m-n} = a^m/a^n$ and $a^{2x} = (a^2)^x$ to rewrite this expression.

Once you simplify the exponent and the numerical coefficient, compare your final expression with the answer options, paying attention to both the base and the coefficient.

In Desmos, enter f(x) = 250*5^x on one line. On the next line, enter h(x) = f(2x - 3) so Desmos will graph the actual $h(x)$ defined in the problem.

On new lines, type each option as its own function, for example A(x) = 2*25^x, B(x) = 250*25^(x-3), C(x) = 50*25^x, and D(x) = 2*5^x. Make sure the syntax matches each choice exactly.

Either visually compare the graph of $h(x)$ with the graphs of $A(x)$, $B(x)$, $C(x)$, and $D(x)$, or use a table (click the gear icon next to each function and select "Table") to compare their $y$-values at several $x$-values. The correct equation for $h(x)$ will match $h(x)$’s graph and table exactly for all tested points.

We are told that $f(x)=250(5)^x$ and $h(x)=f(2x-3)$.

Wherever $x$ appears in $f(x)$, replace it with $2x-3$ to get an expression for $h(x)$:

Now the task is to simplify $250 \bigl(5^{2x-3}\bigr)$.

Use the rule $a^{m-n} = \dfrac{a^m}{a^n}$ to separate the exponent:

So

Notice that $5^{2x}$ can be written as $(5^2)^x$ and $5^2 = 25$:

Substitute this into the expression for $h(x)$:

Since $5^3 = 125$, this becomes

Now just simplify the numerical coefficient $\dfrac{250}{125}$.

Compute the fraction:

So

This is the same as $h(x) = 2(25)^x$, which matches answer choice C.