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*(1)/(1.5^(0.6))`
`V(3)=(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

`(12500)/(25000)=1.5^(-0.2t)`
`ln((12500)/(25000))=ln(1.5^(-0.2t))`
`ln((1)/(2))=-0.2tln(1.5^)`
`(ln((1)/(2)))/(-0.2ln(1.5))=t`
`8.5475=t`

then t when v=12500 is

t=8.55