In this problem, we have an exponential growth function of the form
[tex]y=a(b)^x[/tex]
where
a=10 bacteria (initial value at 2 pm)
b is the base of the exponential function
[tex]y=10(b)^x[/tex]
Find out the value of b
we know that
For x=0 (2 pm), y=10 bacteria
At 5 pm
y=33,750 bacteria
x=(5 pm-2 pm)=3 hours
substitute in the exponential equation
[tex]33,750=10(b)^3[/tex]
Solve for b
[tex]b^3=\frac{33,750}{10}[/tex][tex]\begin{gathered} b=\sqrt[3]{\frac{33,750}{10}} \\ b=15 \end{gathered}[/tex]
the equation is
[tex]y=10(15)^x[/tex]
Part B
At 7 pm
x=(7 pm-2 pm)=5 hours
substitute
[tex]\begin{gathered} y=10(15)^5 \\ y=7,593,750\text{ bacteria} \end{gathered}[/tex]
