Example 6 from Algebra and Trigonometry, 13.3 Geometric Sequences

Solving Application Problems with Geometric Sequences

In 2013, the number of students in a small school is 284. It is estimated that the student population will increase by 4% each year.

ⓐWrite a formula for the student population.
ⓑEstimate the student population in 2020.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. ⓐ
  The situation can be modeled by a geometric sequence with an initial term of 284. The student population will be 104% of the prior year, so the common ratio is 1.04.
  
  Let $P$ be the student population and $n$ be the number of years after 2013. Using the explicit formula for a geometric sequence we get
  $P_{n} = 284 \cdot {1.04}^{n}$
2. ⓑ
  We can find the number of years since 2013 by subtracting.
  
  $2020 - 2013 = 7$
  
  We are looking for the population after 7 years. We can substitute 7 for $n$ to estimate the population in 2020.
  
  $P_{7} = 284 \cdot {1.04}^{7} \approx 374$
  The student population will be about 374 in 2020.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

A business starts a new website. Initially the number of hits is 293 due to the curiosity factor. The business estimates the number of hits will increase by 2.6% per week.

ⓐWrite a formula for the number of hits.
ⓑEstimate the number of hits in 5 weeks.

How did it go?

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

A business starts a new website. Initially the number of hits is 293 due to the curiosity factor. The business estimates the number of hits will increase by 2.6% per week.

ⓐWrite a formula for the number of hits.
ⓑEstimate the number of hits in 5 weeks.

Solution

Your turn

Solution

Your turn