| Year | Subscriptions sold |
|---|---|
| 2012 | 5,600 |
| 2013 | 5,880 |
The manager of an online news service received the report above on the number of subscriptions sold by the service. The manager estimated that the percent increase from 2012 to 2013 would be double the percent increase from 2013 to 2014.
How many subscriptions did the manager expect would be sold in 2014?
A table of yearly counts paired with a comparison of growth rates signals a percent increase problem. Divide the first increase by its starting count, then reverse “double” to find the next rate. Apply that rate to the later count, the new starting amount, in Desmos. Halving the number of subscriptions gained instead of the percent misses that change of base.
Hints
- Hint 1
A percent increase compares the gain with where it started. Subtract the 2012 count from the 2013 count, then divide by the 2012 count. What percent do you get?
- Hint 2
The manager says the earlier rate is double the later rate. Once you know the 2012-to-2013 rate, what one operation gives the rate for 2013 to 2014?
- Hint 3
An increase adds to the full starting amount: the new count is of the old count when the increase is . Use the 2013 count as the base for the next increase.
Step-by-step
Find the rates, then apply the second one
Step 1Find the first percent increase
A percent increase is the gain divided by the starting amount. The count rose from to , so divide the difference by the 2012 starting count. Type in Desmos. It displays , or .
- Step 2
Find the rate the manager expects next
The manager says the earlier percent increase is double the later one, so halve the rate:
Don't halve the number of subscriptions added. The next percent increase will be taken of a different starting count.
- Step 3
Apply the rate to the 2013 count
The 2014 increase starts from the 2013 count, . Each year's percent increase uses that year's starting count. Keep of that count and add , so type in Desmos. It prints , the number of subscriptions the manager expected to sell in 2014. Choice B.