Question

a virus is spreading around brookfield. at the moment, 685 people are infected. if the virus is spreading at a rate of 13% each day, how many people in all will have caught the virus in 3 days? if necessary, round your answer to the nearest whole number. people submit

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is \( A = P(1 + r)^t \), where \( A \) is the final amount, \( P \) is the initial amount, \( r \) is the growth rate (in decimal), and \( t \) is the time in days.

Step2: Convert the growth rate to decimal

The growth rate \( r = 13\% = 0.13 \).

Step3: Substitute the values into the formula

We have \( P = 685 \), \( r = 0.13 \), and \( t = 3 \). So, \( A = 685(1 + 0.13)^3 \).

Step4: Calculate \( (1 + 0.13)^3 \)

First, \( 1 + 0.13 = 1.13 \). Then, \( 1.13^3 = 1.13\times1.13\times1.13 = 1.442897 \).

Step5: Calculate the final amount \( A \)

Multiply \( 685 \) by \( 1.442897 \): \( A = 685\times1.442897 \approx 988.48 \).

Step6: Round to the nearest whole number

Rounding \( 988.48 \) to the nearest whole number gives \( 988 \).

Answer:

988