Question

In the year 2020, there were 14.02 billion cell phones in use worldwide. In 2022, the number

increased to 15.96 billion worldwide.

a. What is the average rate of change in the number of worldwide cell phones?

b. Using 14.02 as the initial amount, write a linear equation that models the number of
worldwide cell phones. Make sure to define the variables.

C.If the rate stays the same, predict the number of cell phones that will be in use worldwide
in the year 2027.

Answer 1

Explanation:

a. The average rate of change in the number of worldwide cell phones can be calculated as:

Average rate of change = (change in number of cell phones) / (change in time)

The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,

Average rate of change = 1.94 billion / 2 years = 0.97 billion/year

So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.

b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:

C(t) - 14.02 = 0.97t

Simplifying, we get:

C(t) = 0.97t + 14.02

So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.

c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).

C(7) = 0.97(7) + 14.02 = 20.83 billion

Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.