Exponential Growth and Decay - Questions - Class Mathematics School Portal

Exponential Growth and Decay - Questions

Question 1

The number of rabbits in a colony is given by $N=80{(1.04)^t}$, where $t$ is in days. How many rabbits were initially in the colony?

Answer

$80$

Worked Solution

Question 2

A house purchased for $\$600000$ is expected to grow at $8\%$ per year. What would the house be worth after 10 years?

Answer

$\$1295355$

Worked Solution

Question 3

A car is bought for $\$50000$, it decreases in value by $12\%$p.a. What is the cars value after 4 years?

Answer

$\$29984.77$

Worked Solution

Question 4

A painting was bought for $\$5000$. In 2 years, the painting was worth $\$6000$. What was the growth rate?

Answer

9.5% p.a

Worked Solution

Question 5

A $10000~\text{L}$ tank is leaking at 5% per hour. How long will it take for the tank to be half full?

Answer

13.5 hours

Worked Solution

Question 6

In Victoria, a reserve is set aside for the breeding of numbats. The expected population after $t$ years is given by $P=40 \times 1.25^t$

What is the expected size of the colony after $8$ years?

Answer

$P=238$

Worked Solution

Question 7

Boiling water is left in a pot to cool. After $t$ minutes, its temperature is given by $T=100 \times 0.75^{t \,\,\,\circ} \text{C}$.

i) Find the initial temperature of the water

ii) Find the water temperature after $5$ minutes ( to the nearest $^\circ \text{C }$)

Answer

i) $100^\circ \text{ C}$

ii) $24^\circ \text{ C}$

Worked Solution

Exponential Growth and Decay - Questions

The number of rabbits in a colony is given by \(N=80{(1.04)^t}\), where \(t\) is in days. How many rabbits were initially in the colony?

A house purchased for \(\$600000\) is expected to grow at \(8\%\) per year. What would the house be worth after 10 years?

A car is bought for \(\$50000\), it decreases in value by \(12\%\)p.a. What is the cars value after 4 years?

A painting was bought for \(\$5000\). In 2 years, the painting was worth \(\$6000\). What was the growth rate?

A \(10000~\text{L}\) tank is leaking at 5% per hour. How long will it take for the tank to be half full?

In Victoria, a reserve is set aside for the breeding of numbats. The expected population after \(t\) years is given by \(P=40 \times 1.25^t\)

What is the expected size of the colony after \(8\) years?

Boiling water is left in a pot to cool. After \(t\) minutes, its temperature is given by \(T=100 \times 0.75^{t \,\,\,\circ} \text{C}\).

i) Find the initial temperature of the water

ii) Find the water temperature after \(5\) minutes ( to the nearest \(^\circ \text{C }\))

Exponential Growth and Decay - Questions

The number of rabbits in a colony is given by \(N=80{(1.04)^t}\), where \(t\) is in days. How many rabbits were initially in the colony?

A house purchased for \(\$600000\) is expected to grow at \(8\%\) per year. What would the house be worth after 10 years?

A car is bought for \(\$50000\), it decreases in value by \(12\%\)p.a. What is the cars value after 4 years?

A painting was bought for \(\$5000\). In 2 years, the painting was worth \(\$6000\). What was the growth rate?

A \(10000~\text{L}\) tank is leaking at 5% per hour. How long will it take for the tank to be half full?

In Victoria, a reserve is set aside for the breeding of numbats. The expected population after \(t\) years is given by \(P=40 \times 1.25^t\) What is the expected size of the colony after \(8\) years?

Boiling water is left in a pot to cool. After \(t\) minutes, its temperature is given by \(T=100 \times 0.75^{t \,\,\,\circ} \text{C}\). i) Find the initial temperature of the water ii) Find the water temperature after \(5\) minutes ( to the nearest \(^\circ \text{C }\))

In Victoria, a reserve is set aside for the breeding of numbats. The expected population after \(t\) years is given by \(P=40 \times 1.25^t\)

What is the expected size of the colony after \(8\) years?

Boiling water is left in a pot to cool. After \(t\) minutes, its temperature is given by \(T=100 \times 0.75^{t \,\,\,\circ} \text{C}\).

i) Find the initial temperature of the water

ii) Find the water temperature after \(5\) minutes ( to the nearest \(^\circ \text{C }\))