Growth, decay, half-life and model parameters.
Example 1
A population starts at 400 and grows by 11% each year. Find the modelled population after 1 years. Give your answer to 1 decimal places.
Show worked answer
Answer: 444.0
- Use P(t)=P(0)(1+r)t.
- P(1)=400(1.11)1.
- Rounded answer: 444.0.
Example 2
A substance has half-life 5 hours. Starting from 40g, how many grams remain after 15 hours?
Show worked answer
Answer: 5
- There are 515=3 half-lives.
- Mass =40×(21)3=5g.
Example 3
P(t)=Abt. P(0)=40 and P(2)=40. The growth factor b is positive. Find b.
Show worked answer
Answer: 1
- P(0) gives A=40.
- Divide P(2) by A:b2=1.
- The positive growth factor is b=1.