Exponential Growth Homework: Find y, k, and When Population Reaches 10K

[Incog]

Homework Statement

A bacteria culture starts with 1000 bacteria and grows to a population of 7000 after an hour.

a) Find the size of the population after t hours.
b) Find the size of the population after 3 hours.
c) Find the rate of growth of the population after 3 hours.
d) When will the population reach 10 000?

Homework Equations

y = yoe$^{kt}$

The Attempt at a Solution

a) y = yoe$^{kt}$
7000 = 1000e$^{kt}$
7 = e$^{kt}$
ln7 = kt
ln7/t = k (is this it?)

b) y = yoe$^{kt}$
y = 1000e$^{k(2)}$ (am I on the right track?)

c) I know I have to take the derivative but what do I take the derivative of?

d) No idea.

 

[Redbelly98]

a) y = yoe$$^{kt}$$
7000 = 1000e$$^{kt}$$
7 = e$$^{kt}$$
ln7 = kt
ln7/t = k (is this it?)

You're close. What is the value of t when y = 7000?

 

[akonn8]

IM havng a similar problem with N=Ae^(kt)

N is the number of bcteria in a culture at difrent times (t days) as expressed as a table

T= 0 ... 1 ... 2 ... 3 ... 4 ... 5 .
N= 10^3. 7.4x10^3. 5.5x10^4. 4x10^5. 3x10^6. 2.2x10^7.


it asks to envestigate the process with reference to the function above, I am confused and needs it explained

 

[Redbelly98]

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Redbelly98
Physics Forums Mentor