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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.

2 Answers

2 votes

Answer:

7,022

Explanation:

User Keeda
by
8.0k points
4 votes

Answer:

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

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.

User Kilby
by
8.0k points
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