# Exponential Growth

## 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.

Last edited by a moderator:

Related Calculus and Beyond Homework Help News on Phys.org
Redbelly98
Staff Emeritus
Homework Helper
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?

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, im confused and needs it explained

Redbelly98
Staff Emeritus
Homework Helper
Welcome to Physics Forums.

To ask a question here, you'll need to start a new discussion thread. Also, you'll need to some attempt towards solving the problem -- this attempt need not be a complete or correct solution.

To start a new thread, you first have to be viewing a subforum page showing a list of existing discussion threads. Then simply click on the New Topic button near the upper left area of the page, just above the words "Threads in Forum".

See this figure:

Regards,

Redbelly98
Physics Forums Mentor