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

1MasterySAQ-SExponent laws and propertiess8 marksPaper 2~12 min

The population of a colony of ants,

P

, is modelled by the function

P(t) = 500 \times 3^{kt}

, where

t

is the time in weeks after the colony is first observed. After 4 weeks, the population is 4500 ants.

(a)

Show that

k = \dfrac{1}{2}

. [3 marks]

(b)

Calculate the population after 10 weeks. Give your answer in the form

a \times 3^b

, where

a

and

b

are integers. [1 mark]

(c)

Determine the number of complete weeks it takes for the population to first exceed 1 000 ants. [4 marks]

Solutions

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