A population, `P`, is to be modelled using the function `P = 2000 (1.2)^t`, where `t` is the time in years.
- What is the initial population? (1 mark)
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- Find the population after 5 years. (1 mark)
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- On the axes below, draw the graph of the population against time, showing the points at `t = 0` and at `t = 5`. (2 marks)
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Show Worked Solution
a. `text{Initial population occurs when}\ \ t = 0:`
`P= 2000 (1.2)^0= 2000`
b. `text{Find} \ P \ text{when} \ \ t = 5: `
| `P` | `= 2000 (1.2)^5` |
| `= 4976.64` | |
| `= 4977 \ text{(nearest whole)}` |
♦ Mean mark (c) 48%.
c.
