Question

researchers studied the replication behavior of a certain virus. from an initial 1,000 copies of the virus, the researchers found that the virus population was increasing at a rate of 12% every 4 hours. the number of viruses n is given by the following model, where t is the number of hours after the study began with the 1,000 copies of the virus. n = 1,000(1.12)^(t/4) use the model to predict the number of viruses in 15 hours. round to the nearest whole number. 1,515 × viruses

Explanation:

Step1: Substitute t value

Given $N = 1000(1.12)^{t/4}$, substitute $t = 15$. So we have $N=1000(1.12)^{15/4}$.

Step2: Calculate exponent

First, calculate $\frac{15}{4}=3.75$. Then we need to find $(1.12)^{3.75}$. Using a calculator, $(1.12)^{3.75}\approx1.5377$.

Step3: Calculate N

Multiply by 1000: $N = 1000\times1.5377 = 1537.7$.

Step4: Round result

Rounding $1537.7$ to the nearest whole - number gives $1538$.

Answer:

$1538$