Question

T=T0e^-0.5t show that t=2lnT0/T Hence find t when T0=30 and T=10

Answer 1

\[T=T _{0}e^-0.5t\] \[2\ln*(T _{0}/T)\]

Answer 2

Do you know how to take In of both sides of the equation? That is the first step.

Answer 3

\[\ln T=(-0.5t)LnT _{0}\]

Answer 4

Not quite.
\[\ln (ab)=\ln a+\ln b\]
Therefore:
\[\ln T=\ln T _{0}-0.5t\]
Note: \[\ln e ^{-0.5t}=-0.5t\]

Answer 5

The original equation can be written as follows:
\[T=T _{0} \times e ^{-0.5t}\ ..........(1)\]
Taking natural logs of both sides of (1) we get:
\[\ln T=\ln T _{0}+\ln e ^{-0.5t}\ .........(2)\]
But\[\ln e ^{-0.5t}=-0.5t\]
Therefore we can rewrite (2) as:
\[\ln T=\ln T _{0}-0.5t\ .......(3)\]

Answer 6

@Abmon98 Does that explanation help you to understand?

Answer 7

yes

Answer 8

Good! Equation (3) can be rearranged as follows:
\[0.5t=\ln T _{0}-\ln T\ .........(4)\]
Can you make the right hand side of (4) a single Ln ?

Answer 9

Hint:
\[\ln a-\ln b=\ln \frac{a}{b}\]

Answer 10

oh now i get it thank you so much

Answer 11

You're welcome :)