Question

Plz help me, thank you

A bacteria culture starts with 40 bacteria and the number doubles every 20 mins.
write an equation of an exponential function that models the described situation.

plz show me the working.

Answer 1

`P=40(1.03526)^(t)`

Explanation:

Exponential Growth

The natural growth of some magnitudes can be modeled by the equation:

`P=P_o(1+r)^(t)`

Where P is the actual amount of the magnitude, Po is its initial amount, r is the growth rate and t is the time.

The initial number of bacteria is Po=40 and it doubles (P=2Po) at t=20 min. With that point we can find the value of r:

`2P_o=P_o(1+r)^(20)`

Simplifying:

`(1+r)^(20)=2`

Solving for 1+r:

`1+r=\sqrt[20]{2}`

`1+r=1.03526`

The exponential function that models the situation is:

`\mathbf{P=40(1.03526)^(t)}`