Question

Solve 270=3e^2.4K to the nearest hundredth

If you can solve this for me could you please give steps so I can understand, please and thank you so much!

Answer 1

Given:

The equation is:

`270=3e^(2.4K)`

To find:

The solution for the given equation to the nearest hundredth.

Solution:

We have,

`270=3e^(2.4K)`

Divide both sides by 3.

`(270)/(3)=e^(2.4K)`

`90=e^(2.4K)`

Taking ln on both sides, we get

`\ln (90)=\ln e^(2.4K)`

`\ln (90)=2.4K`
`[\because \ln e^x=x]`

Divide both sides by 2.4.

`(\ln (90))/(2.4)=K`

`(4.4998)/(2.4)=K`
`[\because \ln (90)\approx 4.4998]`

`1.874916667=K`

Round the value to the nearest hundredth (two decimal place)

`K\approx 1.87`

Therefore, the value of K is 1.87.