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

NameDate

Figure — use these to answer the problems

Push the base above 1 for growth and below 1 for decay, then watch how fast the curve leaves the screen.

y = 1 · 2^x + 0

a, starting amount1

b, growth factor2

Figure 1

Straightforward practice. Get the method working first.

5 problems

A 25% annual rise. What is the growth factor?
Answer
2
What distinguishes exponential change from linear change?
- It multiplies by a fixed factor instead of adding a fixed amount.
- It is always faster from the start.
A 20% annual rise. What is the growth factor?
Answer
A 30% annual fall. What is the decay factor?
Answer
$200 at 50% growth for 2 years. Final amount in dollars?
Answer

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
7
2 = 1.07ᵗ. Which operation isolates t?
- Take a logarithm of both sides.
- Divide both sides by 1.07.
160 g halves every hour. Grams left after 4 hours?
Answer

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.
Write each item under the heading it belongs to: Saving $50 every week · A balance growing 6% each year · A car losing 15% of its value each year · A tank filling at 3 litres a minute
Linear
Exponential
$1000 at 100% growth for 3 years. Final amount in dollars?
Answer
The Savings
$500 at 10% compounded annually. What is the balance after 2 years, in dollars?
Answerdollars
The Half-Life
A sample of 80 g halves every hour. How many grams remain after 3 hours?
Answerg