There is a population of 9,000 bacteria in a colony.
If the number of bacteria doubles every 245 hours, what will the population be 980 hours from now?
Recall that the exponential growth formula is given by
[tex]y=a\cdot b^x[/tex]Where a is the initial population, b is the rate of growth, and x is the time.
For the given case, we have
a = 9,000
b = 2 (doubles)
x = 980/245 = 4
Let us substitute these values into the above formula
[tex]\begin{gathered} y=a\cdot b^x \\ y=9,000\cdot2^4 \\ y=9,000\cdot16 \\ y=144,000 \end{gathered}[/tex]Therefore, the population of the bacteria will be 144,000 after 980 hours from now.
