Question

For the following in functions of the quantity of t minutes

Answer 1

Part A

Given

`Q(t)=400(2)^{(t)/(4)}`

Solution

We ask to double the time i.e

`\begin{gathered} 800=400(2)^{(t)/(4)} \\ \text{Divide both sides by 400} \\ (800)/(400)=(400)/(400)(2)^{(t)/(4)} \\ \\ 2^1=(2)^{(t)/(4)} \\ \\ 1=(t)/(4) \\ \\ \text{cross multiply} \\ t=1*4 \\ t=4 \end{gathered}`

Part B

Given

`y=10((1)/(2))^{(t)/(12)}`

Solution

The half-life would be 5

`\begin{gathered} y=10((1)/(2))^{(t)/(12)} \\ 5=10((1)/(2))^{(t)/(12)} \\ \text{divide both sides by 10} \\ \\ (5)/(10)=(10)/(10)((1)/(2))^{(t)/(12)} \\ \\ (1)/(2)=((1)/(2))^{(t)/(12)} \\ \\ 1=(T)/(12) \\ \text{cross multiply} \\ T=1*12 \\ T=12 \end{gathered}`