Mathematical Methods · Unit 2 · Exponential functions · Introduction to exponential functions
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A savings account initially contains $2,500. The balance, B (dollars), is modelled by the function \[ B = 2{,}500 \times 1.04^t \] where \( t \) is the number of years since the account was opened. The time taken for the balance to reach $5,000 is closest to
A radioactive substance decays according to the model $$N(t) = N_0 \times 2^{-t/30}$$ where $$N(t)$$ is the mass (in grams) remaining after $$t$$ days, and $$N_0$$ is the initial mass. If the initial mass is 480 g, determine: (a) the mass remaining after 15 days (b) the time taken for the mass to decay to 120 g.
A bacterial culture starts with an initial population of 500 cells. The population grows according to the exponential model $P(t) = 500 \times 2^{0.25t}$, where $P(t)$ is the population at time $t$ hours. (a) Calculate the population after 4 hours. [1 mark] (b) Determine the time taken for the population to reach 4,000 cells. Give your answer to the nearest 0.1 hour. [2 marks]