Revisit the exponential growth and compound interest formulas from Lesson 4, but now with the power of logarithms. Learn what each variable represents and how to identify common growth and decay factors from real-world descriptions.
Lesson 3.9 of Exponents & Logarithms in Math 30-1 — Alberta curriculum lessons.
Building on Lesson 4. You actually used exponential growth and decay formulas back in Lesson 4. At that point, the variable was always in a place you could solve for directly.
But now that you understand logarithms, you can solve for the variable even when it's trapped in the exponent. That's the new skill this lesson adds — and it changes what kinds of questions are actually answerable.
The two formulas you need to know are below. One is on your formula sheet; one is not.
In Lesson 4 you used the compound interest formula to find A or P. Now that you know logarithms, you can also solve for t, the time. The variable is in the exponent, so once you isolate the exponential, you convert to logarithmic form or take log of both sides to get t out.
Step 1: Identify all the values. P = 500 (initial investment)
r = 0.08 (8% written as a decimal)
n = 2 (semi-annually means twice per year)
t = t (what we're leaving as the variable)
Step 2: Substitute into A = P(1 + (r)/(n))^(nt). V = 500(1 + (0.08)/(2))^(2t)
V = 500(1.04)^(2t)
Question. Jen invested 500 in an account that earns interest at 8%/a, compounded semi-annually.
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