Unit 9.4 Practical Applications of Logarithmic Functions
Practical Applications
Logarithmic functions are used in many areas in the real world. From radioactivity behavior, bacterial growth, finance, and even detective work. There are some tips to reading a word problem containing a logarithmic function
- Read the problem carefully
- Determine what quantities are given, and what needs to be found
- Identify relevant information
- Check for what the question is asking. Is it growth or decay? Is it continuous or non continuous?
- Set up the equation
- Solve
Solving a word problem containing a logarithmic function
If you put $0.93 in a bank that compounds annually at a rate of 2.25% per year and don’t add any additional money to it, how long will it be for that amount to reach $4.28 billion to the nearest whole year?
Given values:
- P0 = $0.93
- r = 2.25% = 0.0225
- PF = $4.28 billion = 4.28 x 109
Values we need to find:
- time (t)
We will be using the non-continuous exponential growth function since it compounds annually and it is adding to the initial amount
PF = P0 (1 + r)t
[latex]4.28\times{10}^9=0.93{(1+0.0225)}^t[/latex]
[latex]\frac{4.28\times{10}^9}{0.93}={1.0225}^t[/latex]
[latex]\log_{1.0225}\left(\frac{4.28\times{10}^9}{0.93}\right)=\log_{1.0225}({1.0225}^t)[/latex]
t = 999.96 ≈ 1000 years