Question

The number of people in a town of 95,000 who have heard an important news bulletin within t hours of its first broadcast is given by N(t)=95,000(1−e −0.3t). Find the rate of change of the number of informed people at the following times. (Round your answers to the nearest integer.)

a. t = 1 hour
b. t = 2 hours
c. t = 3 hours
d. t = 4 hours

Answer 1

To find the rate of change of the number of informed people, we take the derivative of the function N(t)=95,000(1-e^(-0.3t)) and evaluate it at t=1,2,3, and 4 hours, rounding off to the nearest integer.

Step-by-step explanation:

Rate of Change of the Number of Informed People

The question involves finding the rate of change of the number of informed people in a town after the broadcast of important news. The function given is N(t) = 95,000(1 − e−0.3t), and we are asked to determine this rate at t = 1, 2, 3, and 4 hours. To do this, we need to take the derivative of N(t) with respect to t, which represents the rate of change at any given time t.

The derivative of N(t) is N’(t) = 95,000 × 0.3 × e−0.3t. Now, we can calculate the rate of change for each given time by substituting the values of t into this derivative:

1. For t = 1 hour: N’(1) = 95,000 × 0.3 × e−0.3(1)
2. For t = 2 hours: N’(2) = 95,000 × 0.3 × e−0.3(2)
3. For t = 3 hours: N’(3) = 95,000 × 0.3 × e−0.3(3)
4. For t = 4 hours: N’(4) = 95,000 × 0.3 × e−0.3(4)

After calculating the values in each case, we round off the answers to the nearest integer as requested.