The number of subscribers, f(t), to a website after t years is shown by the equation below:
f(t) = 50(1.75)t
Which conclusion is correct about the number of subscribers to the website?
It increased by 75% every year.
It decreased by 75% every year.
It increased by 50% every year.
It decreased by 50% every year.
The correct conclusion is: It increased by 75% every year.
Enrollment in a school has grown exponentially since the school opened. Below is a graph depicting this growth. Determine the average rate of change from x = 0 to x = 20.
An exponential graph has time in years on the x axis and enrollments on the y axis. An upward rising curve begins at zero comma thirty and passes through twenty comma eighty.
a. 0.4
b. 2.5
c. 5
d. 30
To determine the average rate of change from x = 0 to x = 20, we need to find the change in y (enrollments) divided by the change in x (years).
The change in y is 80 - 30 = 50.
The change in x is 20 - 0 = 20.
The average rate of change is 50/20 = 2.5.
Therefore, the correct answer is b. 2.5.
The annual growth of Jason's spider collection is represented by the table. What does the 3 represent?
x 0 2 4
f(x) 3 12 48
a. The number of new spiders each year
b. The common ratio of spider growth
c. The number of spiders Jason started with
d. The average rate of change of spider growth each year
The 3 in the table represents the number of spiders Jason started with.
This can be determined by looking at the value of f(x) when x = 0, which is 3.
The correct conclusion about the number of subscribers to the website is: "It increased by 75% every year."
To determine the correct conclusion about the number of subscribers to the website, let's analyze the equation:
f(t) = 50(1.75)^t
In this equation, the term (1.75)^t represents the rate of growth or decline.
If the exponent t is positive, the number of subscribers will increase. Conversely, if the exponent t is negative, the number of subscribers will decrease.
Now, let's examine the base of the exponent, which is 1.75.
If the base is greater than 1, the number of subscribers will increase over time. If the base is less than 1, the number of subscribers will decrease.
In this case, the base is 1.75, which is greater than 1. Therefore, the number of subscribers will increase over time.
Based on this analysis, the correct conclusion is:
The number of subscribers to the website increases over time. However, we cannot determine the exact rate of increase without additional information.