Question

What is the rate of growth as a percent for the following function d(x)=23(1.0032)^x

Answer 1

Answer:

g(x), the % growth rate function, is $g(x)=(1.0032^{b-a}-1)*100\ percent$

where b and a are x-values of the function d(x), b > a, and a ≠ 0.

Step-by-step explanation:

So,

Since no two values were specified, I will proceed to make a new function, the % growth rate function g(x), based on the one you have given.

We can define g(x) as follows:

$g(x)=\frac{d(b)-d(a)}{d(a)}*100\ percent$

Where b and a are x-values, b > a, and a ≠ 0.

Substituting the function for values a and b, we get:

$g(x)=\frac{23(1.0032)^b-23(1.0032)^a}{23(1.0032)^a}*100\ percent$

Simplifying, we get:

$g(x)=\frac{1.0032^b-1.0032^a}{1.0032^a}*100\ percent\\ or\\ g(x)=(1.0032^{b-a}-1.0032^{a-a})*100\ percent$

$g(x)=(1.0032^{b-a}-1)*100\ percent$