Question

A magazine has both a print edition and an online edition. The subscription rate continues to increase as the magazine reaches out to new markets. The online subscribers are growing at a rate modeled by y = 360(1.08x) while the print subscribers increass at a rate of y = 55x+360. If x represents time in years, in how many years will online subscribers begin to surpass that of print subscribers? A. in approximately 10 years B. in approximately 12 years C. in approximately 17 years D. the online subscribers will never surpass the print subscribers

Answer 1

Explanation:

The online subscribers will surpass the print subscribers when the number of online subscribers is greater than the number of print subscribers.

Setting the two equations equal to each other, we get:

360(1.08x) = 55x + 360

Solving for x, we get:

x = 12.32

Therefore, the online subscribers will surpass the print subscribers in approximately 12 years. So the answer is B.

Here is the explanation of the solution:

We first set the two equations equal to each other to find the value of x when the number of online subscribers is equal to the number of print subscribers.

Then, we solve for x using a calculator.

The answer is approximately 12 years, so the online subscribers will surpass the print subscribers in approximately 12 years.

Answer 2

C. in approximately 17 years

Explanation:

I used a spreadsheet to calculate the value of each function for years 1 through 20.

online: y = 360(1.08^x)

print: y = 55x + 360

The values are tabulated below.

yr online print

1 388.8 415

2 419.904 470

3 453.49632 525

4 489.7760256 580

5 528.9581076 635

6 571.2747563 690

7 616.9767368 745

8 666.3348757 800

9 719.6416658 855

10 777.212999 910

11 839.3900389 965

12 906.5412421 1020

13 979.0645414 1075

14 1057.389705 1130

15 1141.980881 1185

16 1233.339352 1240

17 1332.0065 1295

18 1438.56702 1350

19 1553.652381 1405

20 1677.944572 1460

The number of online subscriptions is greater than the number of print subscriptions between year 16 and year 17.

Answer: C. in approximately 17 years