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Exponential and Logarithmic Functions · Paper 2 — Free Maths AA HL Practice Questions

1MasterySAQ-SExponent laws and propertiess6 marksPaper 2~9 min
The population of a certain species of bird on an island is modelled by P(t)=500×2ktP(t) = 500 \times 2^{kt}, where tt is the time in years since the start of the study. After 3 years, the population is 800 birds.
(a)
Calculate the value of kk, giving your answer in exact form. [3 marks]
(b)
Determine the number of years it will take for the population to first reach 2000 birds. Give your answer correct to 3 significant figures. [1 mark]
(c)
Find the rate at which the population is increasing at the moment it reaches 2000 birds. Give your answer correct to 3 significant figures. [2 marks]
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