Question

2x - 1 if x < 0Evaluate g (4) for g(x)for g(x) = x²W√xif 0 ≤ x ≤ 5.if x > 5

Answer 1

Solution

Question A:

$\begin{gathered} \text{ To find the rate we compare with the equation below:} \\ A=P(1+r)^t \\ \\ \text{ Thus, } \\ 1+r=0.9 \\ \text{ Subtract 1 from both sides} \\ r=0.9-1 \\ r=-0.1 \end{gathered}$

- Rate of depreciation is 10%

Question B:

$\begin{gathered} v=34000(0.9)^t \\ \text{ when } \\ v=\frac{34000}{2}=17000 \\ \\ 17000=34000(0.9)^t \\ \text{ Divide both sides by 34000} \\ 0.5=(0.9)^t \\ \text{ Take the natural log of both sides} \\ \ln0.5=t\ln0.9 \\ \\ \therefore t=\frac{\ln0.5}{\ln0.9} \\ \\ t=6.578813...\approx6.58years \end{gathered}$

- The number of years is 6.58years