Question

Hi could somebody please help me answer this question? Thank youuu

Answer 1

Given:

`\ln(y-8)=-2x+\ln C`

To find:

y as a function of x.

Solution:

We have,

`\ln(y-8)=-2x+\ln C`

It can be written as

`\ln(y-8)=\ln e^(-2x)+\ln C`
`[\because \ln e^x=x]`

`\ln(y-8)=\ln (Ce^(-2x))`
`[\because \ln (ab)=\ln a+\ln b]`

On comparing both sides, we get

`y-8=Ce^(-2x)`

Adding 8 on both sides, we get

`y=Ce^(-2x)+8`

Therefore, the equation function is
`y=Ce^(-2x)+8`.