Question

A culture of bacteria contains 150 bacteria at time zero. Find the number of bacteria after 5 hours if their number doubles every hour.

I know this problem is simple but I'm wondering if someone could solve this with a formula that i can use on more difficult problems? thanks!

Answer 1

So here you can use an exponential equation of \[y=P(r)^x\]
Where P is the initial number, r is the rate of change, and x is the time
So P is 150 because that's what you start with, and r is 2 because you double it
You would substitute 5 for x and solve

Answer 2

ah ok thank you so much!!

Answer 3

if we start off, with, say... some value
and then we double it on the next
so, say we start with 7
so \(\begin{array}{llll}
value&doubled
\\\hline\\
7&7\cdot 2\implies 7(2^1)\\
(7\cdot 2)&(7\cdot 2)\cdot 2\implies 7(2^2)\\
(7\cdot 2\cdot 2)&(7\cdot 2\cdot 2)\cdot 2\implies 7(2^3)\\
...&....
\end{array}\)

notice, what the equation would be?

Answer 4

it just so happens that in your case, is 150, not 7
but if you set 2 with an exponential of 0, you'll see what that'd give you

Answer 5

ohhhhh ok

Answer 6

thanks i really appreciate that