New Zealand
Level 8 - NCEA Level 3

Exponential Growth and Decay

Interactive practice questions

Niger's population, $t$t years after the year 2000 is modelled by $P=17.7e^{0.0078t}$P=17.7e0.0078t, where $P$P is the number of millions of people.

a

State the population of Niger in the year 2000.

b

State the continuous growth rate used in this model.

c

Find Niger's population in 2005.

Give your answer to one decimal place.

d

Solve for the number of years, $t$t, it will take for Niger's population to reach $22$22 million.

Give your answer to one decimal place.

e

Solve for the number of years, $t$t, it will take for Niger's population to double.

Give your answer to one decimal place.

Easy
Approx 8 minutes

The growth rate per hour of a population of bacteria is $20%$20% of the current population. At $t=0$t=0 the population is $4000$4000.

Which of the following shows the graph of the population of bacteria over time?

Under certain climatic conditions the number $P$P of blue-green algae satisfies the equation $P=Be^{0.0007t}$P=Be0.0007t, where $t$t is measured in days from when measurement began, and $B$B is constant.

The population of feral cats in a local council district has been monitored since January 2013.

The population $P$P is modelled by $P=6000e^{-0.0018t}$P=6000e0.0018t, where $t$t is the number of years from when the population started being monitored.

Outcomes

M8-12

Form differential equations and interpret the solutions

91578

Apply differentiation methods in solving problems