Question

The initial value of a quantity Q (at year t = 0) is 112.8 and the quantity is decreasing by 23.4% per year. a) Write a formula for Q as a function of t. 2 Edit b) What is the value of Q when t-10? Round to three decimal places.

Answer 1

Answer:

a) $Q(t) = 112.8*(0.766)^{t}$

b) When t = 10, Q = 7.845.

Step-by-step explanation:

The value of a quantity after t years is given by the following formula:

$Q(t) = Q_{0}(1 + r)^{t}$

In which $Q_{0}$ is the initial quantity and r is the rate that it changes. If it increases, r is positive. If it decreases, r is negative.

a) Write a formula for Q as a function of t.

The initial value of a quantity Q (at year t = 0) is 112.8.

This means that $Q_{0} = 112.8$.

The quantity is decreasing by 23.4% per year.

This means that $r = -0.234$

So

$Q(t) = 112.8*(1 - 0.234)^{t}$

$Q(t) = 112.8*(0.766)^{t}$

b) What is the value of Q when t = 10?

This is Q(10).

$Q(t) = 112.8*(0.766)^{t}$

$Q(t) = 112.8*(0.766)^{10} = 7.845$

When t = 10, Q = 7.845.