Question

the flu is starting to hit wildgrove. currently, there are 963 people infected, and that number is growing at a rate of 10.2% per day. overall, how many people will have gotten the flu in 14 days?
if necessary, round your answer to the nearest whole number.
blank people

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 (as a decimal), and $t$ is the time in days.

Step2: Convert the growth rate to a decimal

The growth rate is 10.2%, so $r = \frac{10.2}{100} = 0.102$.

Step3: Substitute the values into the formula

We have $P = 963$, $r = 0.102$, and $t = 14$. So, $A = 963(1 + 0.102)^{14}$.

Step4: Calculate the value inside the parentheses first

$1 + 0.102 = 1.102$.

Step5: Calculate the exponent

Now we need to calculate $1.102^{14}$. Using a calculator, $1.102^{14} \approx 3.827$.

Step6: Multiply by the initial amount

$A = 963 \times 3.827 \approx 963\times3.827 = 3685.401$.

Step7: Round to the nearest whole number

Rounding 3685.401 to the nearest whole number gives 3685.

Answer:

3685