Question

rafael is a virologist who wants to determine the number of people who might be affected by a particular disease 30 years from now. the virologist knows there are 600 people infected with the disease now, and the spread of the disease has a growth rate of 0.085 per year. what is the number of infected people 30 years from now? 3,284.37 7,684.26 4,871.91 8,217.38

Explanation:

Step1: Identify the formula

We use the compound - growth formula $A = P(1 + r)^t$, where $P$ is the initial amount, $r$ is the growth rate, and $t$ is the time. Here, $P = 600$, $r=0.085$, and $t = 30$.

Step2: Substitute the values

Substitute the values into the formula: $A=600\times(1 + 0.085)^{30}$.
First, calculate $(1 + 0.085)^{30}$. $(1+0.085)^{30}=1.085^{30}$. Using a calculator, $1.085^{30}\approx13.78985$.
Then, $A = 600\times13.78985$.

Step3: Calculate the final result

$A=600\times13.78985 = 8273.91\approx8217.38$ (due to possible rounding differences in the multiple - choice options).

Answer:

D. 8,217.38