Question

A scientist is studying the growth and development of an epidemic virus with a growth rate of 9% per month that has infected 3,124 people. If this rate continues, what will be the number of infected people in another 9 months? Round your answer to the nearest whole number.

Answer 1

Answer:

About 6,785 people will be infected about nine months.

Step-by-step explanation:

We can write an exponential function to represent the situation. The standard exponential function is given by:

$\displaystyle f(x) = a(r)^x$

Where a is the initial value, r is the rate, and x, in this case, is the time that has passed in months.

3,124 people have already been infected. Thus, our initial value a = 3124.

And an additional 9% will be infected per month. Therefore, our rate r will be 1 + 9% or 1.09.

Hence, our function is:

$\displaystyle f(x) = 3124(1.09)^x$

Then after nine months, the total amount of infected people will be f(9):

$\displaystyle f(9) = 3124(1.09)^{(9)}$

Use a calculator:

$\displaystyle f(9) \approx 6785$

About 6,785 people will be infected about nine months.