Exponentials and Logarithms

Michael's car is valued after 2 years and after 5 years. $V = Ae^{-kt}$ .

Time (years)	2	5
Value (£)	47200	29200

a.

Explain what the value of $A\,$ represents.

[1]

b.

Show that $ln⁡V=ln⁡A−kt\ln V = \ln A - kt$

[1]

c.

Calculate the value of $A\,$ and the value of $k$

[4]

d.

Use the model to predict the value of the car after 10 years.

[2]

Michael's car is valued after 2 years and after 5 years. $V = Ae^{-kt}$ .

Time (years)	2	5
Value (£)	47200	29200

a.

Explain what the value of $A\,$ represents.

[1]

b.

Show that $ln⁡V=ln⁡A−kt\ln V = \ln A - kt$

[1]

c.

Calculate the value of $A\,$ and the value of $k$

[4]

d.

Use the model to predict the value of the car after 10 years.

[2]

Exponentials and Logarithms Questions