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? 4,871.91 3,284.37 8,217.38 7,684.26

Explanation:

Step1: Identify the formula

We use the exponential - growth formula $N = N_0e^{rt}$, where $N_0$ is the initial number of infected people, $r$ is the growth rate, and $t$ is the time in years.

Step2: Substitute the values

Given $N_0 = 600$, $r=0.085$, and $t = 30$. Substitute these values into the formula: $N=600\times e^{0.085\times30}$.

Step3: Calculate the exponent

First, calculate $0.085\times30 = 2.55$. Then, find $e^{2.55}$. Using a calculator, $e^{2.55}\approx12.8623$.

Step4: Calculate the final number

Multiply $600$ by $e^{2.55}$: $N = 600\times12.8623=7717.38$. The closest answer among the options due to possible rounding differences in the options is $7684.26$.

Answer:

D. $7,684.26$