Question

For the function N= 315/1+14e^-0.23t, find an appropriate window to make a good grap

Answer 1

To draw the appropriate exponential graph for the function N = 315 / (1 + 14e^(-0.23t)), follow these steps: choose a range of values for t, calculate the corresponding values of N, plot the values on the graph, label the axes, find the decay rate and mean, and shade the area representing the probability of less than $0.40.

Step-by-step explanation:

To draw the appropriate exponential graph for the function N = 315 / (1 + 14e^(-0.23t)), follow these steps:

1. Choose a range of values for t that you want to plot on the x-axis. For example, you could choose t values from 0 to 10.
2. Calculate the corresponding values of N for each t value. Plug in the t values into the equation N = 315 / (1 + 14e^(-0.23t)) and calculate N.
3. Plot the t values on the x-axis and the corresponding N values on the y-axis.
4. Label the x-axis as 't' and the y-axis as 'N'.
5. To find the decay rate, look at the coefficient of e in the equation (-0.23 in this case). This represents the rate at which N decreases as t increases.
6. To find the mean, use the equation 1 / (-0.23) = -4.34. This represents the average value of t where N reaches its midpoint.
7. To shade the area representing the probability that one student has less than $0.40, calculate N when t = 0.40 and shade the area below that point on the graph.