The count in a bacteria culture was 200 after 10 minutes and 1300 after 40 minutes. Assuming the count grows exponentially,

Question

What was the initial size of the culture?   

Find the doubling period.t  

Find the population after 100 minutes.   

When will the population reach 12000

Answer 1

Try this

P(t)=P*b^t

this is generic exponential equation, b is base, P is value when t=0

have

1300=P*b⁴⁰

200=P*b¹⁰

b=(13/2)^(1/30) ,,,,b=the thirtieth root of (13/2)

b=1.0644 approx

have 200=P*1.0644¹⁰

P=200/1.0644¹⁰

P=107.14 ,,,,cannot use integer or other calculation will have errors

yay, have equation for population of bacteria at any minute.

P(t)=107.14*1.0644^t

for doubling time

want P(t₂)=2*P(t₁)

2=1.0644^(t2^-t1⁾ ,,,,,the constant 107.14 divides to 1

ln(2)=(t₂-t₁)*ln(1.0644)

t₂-t₁=11.11 minutes approx.

Answer 2

200 = a₀e^11k

1300 = a₀e^40k

6.5 = e^29k

Solve for k

2 = e^kt, use k value from above and solve for t.

Use standard formula for the remaining two.