Assume that the number of bacteria follows an exponential growth model: 𝑃(𝑡)=𝑃0𝑒𝑘𝑡 The count in the bacteria culture was 500 after 15 min and 1500 after 40 min. initial culture size?

Answer 1

P(t) = P₀e^kt; P(15) = P₀e^15k = 500; P(40) = P₀e^40k = 1500; e^25k = 3; k = ln3/25.

So, P₀ = 500/e^(3ln3/5) = 500/3^3/5 = 258

Answer 2

P = P₀e^kt

Need to find P₀

_

1500 = P₀e^40k

500 = P₀e^15k

Divide the two equations

3 = e^40k/e^15k = e^25k

Take log of both sides

25k = ln(3)

k = ln(3)/25

500 = P₀e^15ln(3)/25 = P₀e^3ln(3)/5 = P₀3^3/5

P₀ = 500/3^3/5 ≈ 259

Checking:

259(3)^40/25 ≈1500