Introduction
An introduction to the natural logarithm function, \( y = \ln x \)
Properties of Logarithms and Example 1
Solve \[ 10 = 2^t \] using natural log.
Example 2: Modeling Loyola Tuition, Part 3
In the school year 2013–2014, the annual tuition at Loyola University Maryland was $41,850. Since then it has had an annual growth rate of \( r=2.47\%. \) Assuming this growth rate continues, when will the tuition reach $52,000?
Example 3
A city’s population starts at 600,000 in 2010 and has a continuous growth rate of 5%. What is the population size in 2017?
Example 4
Modified from Section 1.7, Problem 14 in Applied Calculus Edition 5 by Hughes-Hallet et al.
A population, currently 200, is growing at 5% per year.
- Write a formula for the population, \( P, \) as a function of time, \( t, \) years in the future.
- Graph \( P \) against \( t. \)
- Estimate the population 10 years from now.
- (modified) Find the doubling time of the population algebraically.
- (added) Model the same population using a continuous growth rate, compare the graph of this model with the graph from part (b).
