Transform and graph logarithmic functions with translations and reflections. Grade 12.
Lesson 3.4 of Exponents & Logarithms in Math 30-1 — Alberta curriculum lessons.
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.
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.
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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