Can you solve the following word problem?

Question

Suppose a certain type of bacteria increases its population according to the law of exponential growth. There were 120 bacteria on the third day of observation, and 600 bacteria on the fifth day. Approximately how many bacteria was on the Petri dish originally?

Show your solutions please, thanks!

Answer 1

120 = Aoe^3r

Ao= 120/e^3r

600=Aoe^5r

Ao =600/e^5t

600e^5t = 120e^3r

(600/120) = e^5r/e^3r

e^2r = 5

2r =ln5 = 1.609

r = 1.609/2 = 0.805

plug that value for r into either equation

Ao = 120/e^3(0.805) = 120/e^(2.415) = 120/11.19= 10.72 = original amount

r =1.609/2 =-0.805

Ao = 120/e^3(-0.805) = 120/e^(-2.415) = 120/-11.19 = 10.72 original amount

Answer 2

Look up the formula for exponential growth

600 = 120e^2k

5 = e^2k

ln 5= 2k

1.6094 ≈ 2k

0.8047 ≈ k

120 = a₀e^3(0.8047)

Can you calculate and answer?