A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

The function

P(t) = 2000e^0.0011552453t or 2000e^(In2/60)t

Step-by-step explanation:

A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

The function is gotten as:

P(t) = Poe^kt

Where P(t) = Number of the bacteria after t minutes

P(o) = Initial number of the bacteria

e = Euler number

k = Growth rate

t = time

We have to find k

We are told that the culture contains 2000 bacteria initially and doubles every 60 minutes.

Hence,

n(60) = 2 × 2000

n(60) = 4000

This:

4000 = 2000 × e^k × 60

4000/2000 = e^60k

2 = e ^60k

In 2 = In e^60k

In 2 = 60k

k = In2/60

k = 0.011552453

Hence, the function P(t) = 2000e^0.0011552453t or 2000e^(In2/60)t

abby has a greater debt becasue she owea 5 more then alan does

320ft

step-by-step explanation:

120 divided by 3 equals 40

40 times 4=160

160 times 2=320