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
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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 (in decimal), and $t$ is the time in days.
Here, $P = 685$, $r = 0.13$ (since 13% = 0.13), and $t = 3$.

Step2: Substitute the values into the formula

Substitute $P = 685$, $r = 0.13$, and $t = 3$ into the formula:
$$A = 685(1 + 0.13)^3$$

Step3: Calculate the value inside the parentheses first

First, calculate $1 + 0.13 = 1.13$.

Step4: Calculate the exponent

Now, calculate $1.13^3$.
$1.13^3 = 1.13 \times 1.13 \times 1.13 = 1.2769 \times 1.13 = 1.442897$.

Step5: Multiply by the initial amount

Now, multiply $685$ by $1.442897$:
$685 \times 1.442897 \approx 988.484445$.

Step6: Round to the nearest whole number

Rounding $988.484445$ to the nearest whole number gives $988$.

Answer:

988