Question

Which company’s profit shows a greater average rate of change? Company A:
$1.5 million profit in 2010; after 5 years, grew exponentially to $2.5 million.
Company B: profit modeled by P(B) = 1.3(1.15)x

Answer 1

Company B's profit shows greater average rate of change.

Step-by-step explanation:

Consider the equation that represents profit of company A since 2010 is,

$y=ab^x$                  ...... (1)

For 2010, x =0,

That is, A's profit in 2010,

$y=ab^0=a$

According to the question,

$a=1.5$

Now, A's profit after 5 years since 5 years,

$y=ab^5=1.5b^5$

Again according to the question,

$1.5b^5=2.5$

$b^5=\frac{2.5}{1.5}$

Taking log both sides,

$5\log b =\log(\frac{5}{3})$

$\implies b = 1.108$

Substituting values of a and b in equation (1),

The equation that shows company A's profit is $y=1.5(1.108)^x$

We have, the equation that shows company B's profit is $P(B) = 1.3(1.15)^x$

Since an exponential equation $ab^x$ with higher value of b( growth factor ) has greater rate of change,

Also, 1.15 > 1.108

Therefore, $P(B) = 1.3(1.15)^x$ shows greater average rate of change.

#Learn more:

Growth and decay in exponential functions:

https://brainly.in/question/5390978