The count in a bacteria culture was 500 after 15 minutes and 1700 after 40 minutes. Assuming the count grows exponentially,

Question

The count in a bacteria culture was 500 after 15 minutes and 1700 after 40 minutes. Assuming the count grows exponentially,



What was the initial size of the culture? ncorrect  

Find the doubling period. Incorrect  

Find the population after 100 minutes.   

When will the population reach 11000. 

Answer 1

The general formula for exponential equations is:

y= ab^t, where a and b are constants

We know that when t = 15, y= 500

and that when t= 40, y = 1700

Plug these in and get two equations:

500 = ab¹⁵

1700 = ab⁴⁰

Now, all you have to do is solve for this system of equations.

The easiest way of solving this do the second equation divide by the first

(1700/500) = (ab⁴⁰)/(ab¹⁵)

Simplify:

3.4 = b²⁵

b = ²⁵√3.4

Now solve for a:

500 = ab¹⁵

500 = a(²⁵√3.4)¹⁵

500 = a(3.4)^15/25

500 = a(3.4)^0.6

a = 500/(3.4)^0.6

Now that we solved the constants plug them back in to the general formula

y= ab^t

y = 500/(3.4)^0.6 · (²⁵√3.4)^t

We can simplify this up a bit

y = 500/(3.4)^0.6 · (3.4)^t/25

y = 500 · (3.4)^-0.6 · (3.4)^0.04t

y = 500 · 3.4^0.04t-0.6