Question

Which is the initial value that shrinks an exponential growth function by 50%? One-fifth One-fourth One-third One-half

Answer 1

Answer:

One-half

Step-by-step explanation:

Given

Exponential function

Required

The initial value that shrinks the function by $50\%$

An exponential function is represented as:

$y = ab^x$

Where the growth function is:

$r = b^x$

$a \to$ initial value

For the growth function to shrink by x%, then:

$a =1 - x\%$

In this case; x = 50. So, we have:

$a =1 - 50\%$

Express as fraction

$a =1 - \frac{50}{100}$

Take LCM

$a =\frac{100 -50}{100}$

$a =\frac{50}{100}$

Reduce fraction

$a =\frac{1}{2}$