which is the initial value that shrinks an exponential growth function by 50%?\n$\frac{1}{5}$\n$\frac{1}{4}$\…

Explanation:

Step1: Understand exponential growth concept

An exponential function is of the form $y = a\cdot b^x$, where $a$ is the initial - value and $b>1$ for growth. Shrinking the function by 50% means the new function value is half of the original function value when $x = 0$. When $x = 0$, $y=a\cdot b^0=a$. If we want to shrink it by 50%, the new initial - value should be half of the original initial - value.

Step2: Determine the initial value

If the original initial value is considered as 1, and we want to shrink the function by 50% (or make it half of its original value at $x = 0$), the new initial value is $\frac{1}{2}$.

Answer:

$\frac{1}{2}$