The number of reports of a certain virus has increased exponentially since 1960. The number of cases can be approximated using the function $r(t)=207 \mathrm{e}^{0.006 t}$, where $t$ is the number of years since 1960. Estimate the number of cases in the year 2000.
A) 248 cases
B) 197 cases
C) 263 cases
D) 526 cases

Question

Quizplus · Accepted Answer

To find the number of cases in the year 2000, substitute $t = 40$ (since 2000 is 40 years after 1960) into the function: $r(40) = 207 \mathrm{e}^{0.006 \times 40} \approx 263$.

The Number of Reports of a Certain Virus Has Increased r(t)=207e0.006tr(t)=207 \mathrm{e}^{0.006 t}r(t)=207e0.006t

The Number of Reports of a Certain Virus Has Increased $r(t)=207 \mathrm{e}^{0.006 t}$