A population of Tasmanian devils, `D`, is to be modelled using the function `D = 650 (0.8)^t`, where `t` is the time in years.
- What is the initial population? (1 mark)
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- Find the population after 2 years. (1 mark)
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- On the axes below, draw the graph of the population against time, in the period `t = 0` to `t = 6`. (2 marks)
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Show Worked Solution
a. `text{Initial population occurs when}\ \ t = 0:`
`D=650(0.8)^0=650 xx 1= 650`
b. `text{Find} \ D \ text{when} \ \ t = 2: `
`D= 650 (0.8)^2= 416`
♦ Mean mark (c) 48%.
c. `\text{At}\ t=6:`
`D=650(0.8)^6=170.39…`
