Question

question 4 of 25
a colony of bacteria is growing exponentially according to the function below, where t is in hours. what will the approximate number of bacteria be after 6 hours?
b(t)=4·e^{0.8t}
a. 94,251
b. 8602
c. 122
d. 486

Explanation:

Step1: Substitute \(t = 6\) into the function

We have the function \(B(t)=4\cdot e^{0.8t}\). Substitute \(t = 6\) into it, so \(B(6)=4\cdot e^{0.8\times6}\).
First, calculate the exponent: \(0.8\times6 = 4.8\). Then the function becomes \(B(6)=4\cdot e^{4.8}\).

Step2: Calculate the value of \(e^{4.8}\)

We know that \(e\approx2.71828\). Using a calculator, \(e^{4.8}\approx121.51042\).

Step3: Calculate the value of \(B(6)\)

Now, \(B(6)=4\times121.51042\). \(4\times121.51042 = 486.04168\approx486\)

Answer:

D. 486