Building and Solving DE

[Sjsusu]

Hello, my calculus teacher recently assigned us these problems but he has not yet taught Differential Equations. I have been able to solve most of the other questions but I can't seem to figure this one out.
Based on the given information, I assume da/dt= ka
( No variables are given so I chose a as amount of Bacteria present)
However I am confused on what to do after to find a solution for t=6.
Thanks for taking the time to read this, any help is much appreciated.

 

[Harry_the_cat]

\(\displaystyle \frac{da}{dt}=ka\)
\(\displaystyle \int\frac{da}{a} =\int k dt\)
\(\displaystyle ln a = kt + c\)
\(\displaystyle a=e^c e^{kt}\)
Now sub in t=0, a=10 to find c.
Then sub in t=2, a=30 to find k.

Once you have the equation, the rest is easy.

 

[Sjsusu]

\(\displaystyle \frac{da}{dt}=ka\)
\(\displaystyle \int\frac{da}{a} =\int k dt\)
\(\displaystyle ln a = kt + c\)
\(\displaystyle a=e^c e^{kt}\)
Now sub in t=0, a=10 to find c.
Then sub in t=2, a=30 to find k.

Once you have the equation, the rest is easy.

Thank you, after plugging in I got c. I didn't initially realize that the function would become an exponential.