Applications of Exponential Functions

Transform and graph logarithmic functions with translations and reflections. Grade 12.

Lesson 3.4 of Exponents & Logarithms in Math 30-1: Alberta curriculum lessons.

What you'll learn in this lesson

Inside the lesson: a free preview

Why Applications Matter

Every exponential function you've studied has a real-world meaning. Money growing in a bank account, bacteria multiplying in a lab, radioactive material decaying, a car losing value, all of these follow exponential patterns.

This lesson teaches you how to take a word problem, identify the right formula, assign each variable correctly, and solve for whatever the question is asking. There are two formulas you'll use throughout this lesson, knowing when to use each one is the most important skill here.

Formula 1: Compound Interest

Compound Interest Formula. A = P(1 + (r)/(n))^(nt)Used specifically for money problems involving compound interest.

What Each Variable Means. A = the final amount of money

P = the principal: the initial amount invested or borrowed

r = the annual interest rate as a decimal (e.g. 6% → 0.06)

n = the number of times interest is compounded per year

t = the time in years

Compounding Periods: Values of n. Annually → n = 1 (once per year)

Semi-annually → n = 2 (twice per year)

Quarterly → n = 4 (four times per year)

Monthly → n = 12 (twelve times per year)

In plain English: your money grows a little bit every compounding period. The more frequently interest is compounded, the more you earn, because each period you're earning interest on top of previously earned interest.

Worked example: Detailed Example 1: Finding the Final Amount

Question: Mani invested 3,000 for 18 months at 6% per year. Calculate the final amount if interest is compounded:

a) Annually

b) Quarterly

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