Question

The table represents an exponential function.

What is the multiplicative rate of change of the function?

A. 1/5

B. 2/5

C. 2

D. 5

Answer 1

The exponential function is given in the form

$y= a (b)^{x}$

where a is the initial value and b is the multiplicative rate of change

So lets plug the first two values of the table in this function , we get

$2= a(b)^1$

or

$2= ab............................(eqn 1)$

Now plug second

$2/5 = a(b)^2 .............................( eqn2)$

Divide equation 2 by equation 1

$\frac{2=ab}{\frac{2}{5}=ab^2}$

On simplifying we get

$5= \frac{1}{b}$

or

$b=\frac{1}{5}$

So the multiplicative rate of change of the function is

$a) \frac{1}{5}$

Answer 2

The multiplicative rate of change of the function is b=1/5.

We have given that the table represent the exponential function

What is the general form of exponential function?

The exponential function is given in the form

$y=a(b)^x$

where a is the initial value and b is the multiplicative rate of change

So lets plug the first two values of the table in this function , we get

from table y=2 and x=1

$2=a(b)^1\\2=ab....1$

Now plug second from the given table

y=2/5 and x=2

$2/5=a(b)^2\\2/5=ab^{2}....2$

We have to find the value of b.

Therefore divide equation 2 by equation 1

$\frac{2=ab}{2/5=ab^2}$

$5=\frac{1}{b}$

$b=\frac{1}{5}$

So,the multiplicative rate of change of the function is b=1/5.

To learn more about the exponential function visit:

https://brainly.com/question/12940982