Question

10a) in the year 2012, graceville had a population of 1.4 million people and an annual growth rate of 1.35%.
write a function to model graceville’s population with respect to t, the number of years since 2012.
hint: use ( n(t) = n_0 e^{kt} )

Explanation:

Step1: Identify initial population

$N_0 = 1.4$ (million, 2012 baseline)

Step2: Convert growth rate to decimal

$k = \frac{1.35}{100} = 0.0135$

Step3: Substitute into exponential model

Use $N(t)=N_0e^{kt}$ to build the function.

Answer:

$f(t)=1.4e^{0.0135t}$