PRE CALC AB - A new app was downloaded 175 times in its first week. Since then, the number of downloads increased by 16.5% each week.

Question

A new app was downloaded 175 times in its first week. Since then, the number of downloads increased by 16.5% each week.

 

a) Write a continuous exponential growth model to approximate the number of times the app was downloaded.

 

b) Find the number of times the app was downloaded in its 12th week.

Answer 1

Given: New app was downloaded 175 times during the first week.

After the 1st week, downloads increased by 16.5% each week.

Find:

(a) Continuous growth model

(b) Number of times the app was downloaded during week #12.

Solution:

n = week number

An = Number of downloads during week n

A1 = 175

An = 175(1.165)^(n-1)

A12 = 175(1.165)^(11) = 938.91

During week 12, the app was downloaded approximately 939 times.

Answer 2

A = 175(1.165)^t

A = 175(1.165)¹²