Answer:
it takes 24 hours for the bacteria cells to increase to 300
Step-by-step explanation:
WE use the formula
[tex]C= A(b)^{\frac{t}{d}}[/tex]
Where A is the initial amount of bacteria= 100
bacteria doubles every 15 hours so b=2
d= 15 because d is the time taken to double the number
t is the number of hours
c is the number of bacteria after t hours = 300
Plug in all the values and solve for 't'
[tex]300= 100(2)^{\frac{t}{15}}[/tex]
Divide both sides by 100
[tex]3=(2)^{\frac{t}{15}}[/tex]
Now we take log on both sides
[tex]log(3)=log(2)^{\frac{t}{15}}[/tex]
As per log property we can move the exponent before log
log a^m = m log(a)
[tex]log(3)=\frac{t}{15}log(2)[/tex]
Divide both sides by log(2)
[tex]\frac{log(3)}{log(2)} = \frac{t}{15}[/tex]
Multiply both sides by 15
[tex]\frac{log(3)}{log(2)}*15=t[/tex]
t = 23.77
So its approximately 24 hours
