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Mathematical Modelling · Guided Practice

Exponential Relationships

10 questions with answers and video solutions. Try each one before revealing the answer.

1
A population is modelled by P=620(1.06)t\displaystyle P = 620(1.06)^t, where t\displaystyle t is the number of years.
(a) State the initial population.
(b) State the annual percentage increase.
Video solution coming soon
2
A population is modelled by P=620(1.06)t\displaystyle P = 620(1.06)^t, where t\displaystyle t is the number of years.
Calculate the population after 5\displaystyle 5 years.
Give your answer to the nearest whole number.
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3
The value of a car is modelled by V=15000(0.82)t\displaystyle V = 15000(0.82)^t, where t\displaystyle t is the number of years.
State the annual percentage depreciation.
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4
The value of a car is modelled by V=15000(0.82)t\displaystyle V = 15000(0.82)^t, where t\displaystyle t is the number of years.
Calculate the value of the car after 4\displaystyle 4 years.
Give your answer to the nearest pound.
Video solution coming soon
5
The concentration of bacteria, C\displaystyle C, remaining m\displaystyle m minutes after a treatment is modelled by C=900e−0.05m\displaystyle C = 900e^{-0.05m}.
Calculate the concentration after 12\displaystyle 12 minutes.
Give your answer to 1 decimal place.
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6
A colony of bacteria is modelled by N=240e0.08t\displaystyle N = 240e^{0.08t}, where t\displaystyle t is the time in hours.
Calculate N\displaystyle N when t=10\displaystyle t = 10.
Give your answer to the nearest whole number.
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7
A colony of 850\displaystyle 850 insects grows at an effective rate of 4.2%\displaystyle 4.2\% per year.
Calculate the size of the colony after 9\displaystyle 9 years.
Give your answer to the nearest whole number.
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8
The mass of a radioactive sample is modelled by M=500(0.93)d\displaystyle M = 500(0.93)^d, where d\displaystyle d is the number of days.
Calculate the mass after 10\displaystyle 10 days.
Give your answer to 1 decimal place.
Video solution coming soon
9
An animal population is modelled by P=a(b)t\displaystyle P = a(b)^t with b>1\displaystyle b > 1.
Explain why this model must eventually become unrealistic.
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10
2022 Q10
(2, 3)5 Marks

You must refer to the information on 'Mountain gorillas' given in the pre-release material when answering this question.

The 2020 study found that the population of mountain gorillas had increased to 1004.

An expert has stated that if the mountain gorilla population in the Virunga Mountains continues to grow exponentially there will be 1600 gorillas by the year 2032.

(a) Determine if the expert's statement is correct. Give a reason for your answer.

A typical adult mountain gorilla eats 30 kg of food per day.

(b) Estimate the maximum amount of termites and ants (in kg) that a typical mountain gorilla will eat during their adult lifetime.

State any assumptions you have made.

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