Exponential Models and Compound Interest

Growth that feeds on itself.

12 problems · about 23 minutes · F-LE.A.1, F-LE.A.4, A-SSE.B.3

What this lesson teaches

The student builds exponential growth and decay models, including compound interest, and solves for time with logarithms.

Straightforward practice. Get the method working first.

5 problems

A 25% annual rise. What is the growth factor?
Answer 1.25
Why 1.25.
What distinguishes exponential change from linear change?
Answer It multiplies by a fixed factor instead of adding a fixed amount.
Why A fixed multiplier rather than a fixed addition.
A 20% annual rise. What is the growth factor?
Answer 1.2
Why 1 + 0.20.
A 30% annual fall. What is the decay factor?
Answer 0.7
Why 1 − 0.30.
$200 at 50% growth for 2 years. Final amount in dollars?
Answer 450
Why 200 × 1.5 × 1.5.

The same ideas with more to keep track of.

3 problems

A population doubles every 5 years. By what factor does it grow in 15 years?
Answer 8
Why Three doublings.
2 = 1.07ᵗ. Which operation isolates t?
Answer Take a logarithm of both sides.
Why The unknown is in the exponent.
160 g halves every hour. Grams left after 4 hours?
Answer 10
Why 80, 40, 20, 10.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each situation by the kind of change it shows.
Answer Linear: Saving $50 every week, A tank filling at 3 litres a minute · Exponential: A balance growing 6% each year, A car losing 15% of its value each year
Why Adding the same amount is linear; multiplying by the same factor is exponential.
$1000 at 100% growth for 3 years. Final amount in dollars?
Answer 8000
Why Doubling three times.
The Savings: $500 at 10% compounded annually. What is the balance after 2 years, in dollars?
Answer 605 dollars
Why $605.
The Half-Life: A sample of 80 g halves every hour. How many grams remain after 3 hours?
Answer 10 g
Why 10 g.