Model Exponential Growth and Decay

5 questions0m 0s

Learn the skill

In A(t) = A0 x b^t, A0 is the starting amount and b is the multiplier for one time step. A percentage increase p gives b = 1 + p/100; a decrease gives b = 1 - p/100.

Worked example

A model starts at 40 and grows by 50% per step. Its multiplier is 1.5. After two steps the amount is 40 x 1.5^2 = 90, not 40 + 50 + 50.

1. A model starts at 12 and doubles each step. What is its value after 3 steps? Answer

2. A model starts at 160 and halves each step. What is its value after 4 steps? Answer

3. Which multiplier represents a 15% decrease per step? 1.15 0.15 0.85

4. Which sequence has a constant exponential multiplier? 3, 6, 12, 24 3, 6, 9, 12 3, 4, 6, 9

5. For A(t) = 7 x 3^t, what is A(0)? Answer