Mathematics: EXPONENTIALS - LOGARITHMS Topical Past Paper Questions

[Maximum mark: 5] The first term in an arithmetic sequence is 4 and the fifth term is $ \log_{2}625 $. Find the common difference of the sequence, expressing your answer in the form $ \log_2 p $, where $ p \in \mathbb{Q} $.

The population of fish in a lake is modelled by the function $ f(t)=\frac{1000}{1+24e^{-0.2t}},0\leq t\leq30 $, where t is measured in months. (a) Find the population of fish at t = 10. [2] (b) Find the rate at which the population of fish is increasing at t = 10. [2] (c) Find th…

Let $ b=\log_{2}a $, where a>0. Write down each of the following expressions in terms of b. (a) $ \log_{2}a^{3} $ (b) $ \log_{2}8a $ (c) $ \log_{8}a $