Question

Please assist me in answering these math questions. Thank you

Answer 1

given the function

$V=25000*1.5^{-0.2t}$

A) the value when Shiyun bought the car (t=0)

$V(0)=25000*1.5^0$$V(0)=25000*1$$V(0)=25000$

the value when Shiyun bought the car was 25000 USD

b) calculate the Value of the car 3 years after Shiyun bought it (t=3)

$V(3)=25000*1.5^{-0.2(3)}$$V(3)=25000*\frac{1}{1.5^{0.6}}$$V(3)=\frac{25000}{1.2754}=19601.317$

then the Value of the car 3 years after Shiyun bought it was 19601.32 USD

c)calculate time when V is half the value when Shiyun bought it

since the started value is 25000

half of that value is 12500

then

$V=12500=25000*1.5^{-0.2t}$

Solving for t

$\frac{12500}{25000}=1.5^{-0.2t}$$ln(\frac{12500}{25000})=ln(1.5^{-0.2t})$$ln(\frac{1}{2})=-0.2tln(1.5^)$$\frac{ln(\frac{1}{2})}{-0.2ln(1.5)}=t$$8.5475=t$

then t when v=12500 is

t=8.55