Question

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a virus is spreading around kingwood. at the moment, 368 people are infected. if the virus is spreading at a rate of 6% each day, how many people in all will have caught the virus in 5 days? if necessary, round your answer to the nearest whole number. \boxed{} people

Explanation:

Step1: Identify the formula for exponential growth

The formula for exponential growth is $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the growth rate (as a decimal), $t$ is the time in days, and $A$ is the amount after $t$ days.
Here, $P = 368$, $r = 0.06$ (since 6% = 0.06), and $t = 5$.

Step2: Substitute the values into the formula

Substitute $P = 368$, $r = 0.06$, and $t = 5$ into the formula:
$A = 368(1 + 0.06)^5$

Step3: Calculate $(1 + 0.06)^5$

First, calculate $1 + 0.06 = 1.06$. Then, $1.06^5 \approx 1.3382255776$.

Step4: Multiply by the initial amount

Multiply $368$ by $1.3382255776$:
$A = 368 \times 1.3382255776 \approx 492.467$

Step5: Round to the nearest whole number

Rounding $492.467$ to the nearest whole number gives $492$.

Answer:

492