Question

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

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.

$\dfrac{270}{3}=e^{2.4K}$

$90=e^{2.4K}$

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.

$\dfrac{\ln (90)}{2.4}=K$

$\dfrac{4.4998}{2.4}=K$           $[\because \ln (90)\approx 4.4998]$

$1.874916667=K$

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

$K\approx 1.87$

Therefore, the value of K is 1.87.