Exponential growth and decay models · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Exponential change and limiting levels — objective 1

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 20 + 10 e^{- 2 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=20, A=10, k=2\).

Find Q(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Exponential change and limiting levels — objective 1

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 21 + 12 e^{- 3 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=21, A=12, k=3\).

Find Q(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Exponential change and limiting levels — objective 2

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 21 + 12 e^{- 3 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=21, A=12, k=3\).

Find \(\displaystyle Q(\frac{\ln 2}{k})- L\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Exponential change and limiting levels — objective 2

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 22 + 14 e^{- 4 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=22, A=14, k=4\).

Find \(\displaystyle Q(\frac{\ln 2}{k})- L\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Exponential change and limiting levels — objective 3

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 22 + 14 e^{- 4 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=22, A=14, k=4\).

Find Q′(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Exponential change and limiting levels — objective 3

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 23 + 6 e^{- t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=23, A=6, k=1\).

Find Q′(0).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Exponential change and limiting levels — objective 4

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 23 + 6 e^{- t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=23, A=6, k=1\).

Find the limiting value as t increases without bound.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Exponential change and limiting levels — objective 4

Maths4U Original · Short practice

A quantity is modelled by \(Q{\left(t \right)} = 24 + 8 e^{- 2 t}\) for \(\displaystyle t\ge 0\). Here \(\displaystyle L=24, A=8, k=2\).

Find the limiting value as t increases without bound.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Try written exam-style problems →