1. ## calculus homework

Hey just had a problem regarding rates of change.
ill post the whole question so there is no confusion.
" The number of bacteria present in a culture at time t hours after the beginning of an experiment is denoted by N. The relationship between N and t is modelled by N=10(1+3/2t)*3 (that is 10 multiply 1 plus 3 over 2 t to the power of 3) At what rate per hour will the number of bacteria be increasing when t=6?

im assuming the chain rule must be used but i cant find the other differential i need to use... any help would be greatly appreciated

thanks

2. Hello, Yesme!

The number of bacteria present in a culture at time $\displaystyle t$ hours
after the beginning of an experiment is denoted by $\displaystyle N.$
The relationship between $\displaystyle N$ and $\displaystyle t$ is modelled by N=10(1+3/2t)*3
(that is 10 multiply 1 plus 3 over 2 t to the power of 3)
At what rate per hour will the number of bacteria be increasing when $\displaystyle t=6$ ?

im assuming the chain rule must be used . . . . Yes!
but i cant find the other differential i need to use. . . . . other differential?
I assume the function is: .$\displaystyle N \;=\;10\left(1 + \frac{3}{2}t\right)^3$

Then: .$\displaystyle \frac{dN}{dt} \;=\;30\left(1 + \frac{3}{2}t\right)^2\!\!\cdot\frac{3}{2} \;=\;45\left(1 + \frac{3}{2}t\right)^2$

Now substitute $\displaystyle t = 6.$

3. ## thanks

oh right, i assumed that you had to find another differential where it was something like:

dN/dx multiply dx/dt so then u get dN/dt but i guess i never read the question properly....oops