Two software companies are planning to launch a learning application on the same day.

company a predicts that their application will be downloaded 400 times on the first day and that the number of downloads will increase at a rate of 50% per day. this relationship is represented by function f below, where x is the number of days since the launch of the application.

f(x) = 400(1.5)^x

company b predicts that their application will be downloaded 500 times on the first day and that the number of downloads will increase at a rate of 40% per day. this relationship is represented by function g below, where x is the number of days since the launch of the application.

g(x) = 500(1.4)^x

both companies record their number of downloads from the release until 4 days after the release.

company a had 450 downloads on the first day, and the number of downloads increased at a rate of 25% per day. company b had 400 downloads on the first day, and the number of downloads increased at a rate of 60% per day.

use the information above to complete the given statements.

We have that we are given 4 formulas for the products; there are split in 2, one for each company and they are also split in 2 on whether they are predictions or date. We need to substitute in x=4 days for all of them to calculate the value after 4 days after the launch (initial day counts for x=0).
For company A, the actual average downloads per day were: for x=0 (day 1), x=1, x=2, x=3, x-4:
f(0)=450, f(1)=562.5, f(2)=703, f(3)=879, f(4)=1099
To find the average download per days, we have that we divide the final downloads f(4) by the number of days, 4. This yields 275 downloads per day.
For the prediction formula f(x)=400*1.5^x, if we substitute x=4 we get 2025 downloads. This yields on average 506 downloads per day.
Thus, the difference is 231 downloads per day and we have a decrease in the data (from predicted to actual downloads).

For company B, the same procedure for the actual data yields: g(4)=2621 downloads after 4 days, hence 655 downloads on average; the prediction data yields  500*1.4^4=1921 and on average 480 downloads per day; the difference is around 175 (174 due to rounding errors) downloads per day and it is still a decrease (predictions are lower).

Thus, company B was more accurate.

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