Question

Part 3: Solve a real-world problem using a cube root functionOnce Isabel rented the warehouse space, she decided to post ads on several social media sites toadvertise her online bookstore. represent the number ofmonths the ads have been posted. Isabelfinds that the function below describes the number of books sold as a function of the number ofmonthsher ads have been posted.f(x) 1000 (VX) 1000a) How many books were sold after 8 months?b) Graph the function.

Answer 1

After 8 months, Isabel sold 2000 books. The cube root function plotted as a graph would start steep and flatten out over time. Cube root calculations can be critical in solving different equilibrium problems.

Step-by-step explanation:

Isabel's problem can be solved by plugging in the specific values into her cube root function which describes the number of books sold as a function of the number of months her ads have been posted.

1. To find how many books were sold after 8 months, we calculate f(8) = 1000(∛8). Since the cube root of 8 is 2, we then have 1000(2) = 2000. Therefore, Isabel sold 2000 books after 8 months.
2. Graphing the function, we would plot the cubic root of 'x' multiplied by 1000 for each value of 'x' representing the number of months. The shape of the graph would start off steep and gradually level out as 'x' increases.

When performing these calculations, it's imperative to know how to use cube roots on a calculator as they may be required in solving various types of equilibrium problems.

Answer 2

x = number of months the ads have been posted
f(x) = number of books sold w/in the months the ads have been posted

f(x) = 1000(∛x) + 1000

Books sold after 8 months

f(8) = 1000(∛8) + 1000
f(8) = 1000(2) + 1000
f(8) = 2000 + 1000
f(8) = 3000

3000 books were sold after 8 months