# Thread: Need help with exponential growth solutions!

1. ## Need help with exponential growth solutions!

hi guys, i could really use your help right now. i just started school at a university 2 weeks ago and i transferred out of one of my classes into a new class. the class im in now is environmental biology and i am confused on a few problems the teacher gave out. the math is basic exponential growth and input-output relations....:

1.) (a) what is the doubling time for a population of rabbits growing at 5% annually?

(b) what is the doubling time if the annual growth rate is 10%?

2.) assume you are growing bacteria in a large petri dish. if you start with 10 g of bacteria growing exponentially at a rate of 10% per hour, then what is quantity of bacteria at the end of 10 hours?

4.) if you have 10,000 fish and want to grow the stock to 100,000 fish, then how long will it take if the growth rate is 7% per year? how long if the growth rate is 2% per year?

5.) what is the input-output relation for the following examples(e.g., 1>0,1<0, or 1=0)? for those at steady state, calculate the average resident time, and for those that are shrinking determine when the stock will be depleted.

1.) $1000/mo.----->[Bank account$5000]------>\$1500/mo----->

i have class tomorrow morning(in 7 hours) and would love some help asap. thanks in advance!

2. Originally Posted by Uniballer

1.) (a) what is the doubling time for a population of rabbits growing at 5% annually?
$A = A_0 \times 1.05^t$

Find where

$A = 2\times A_0$

$2\times A_0 = A_0 \times 1.05^t$

$2= 1.05^t$

$t= \dots$

3. can anyone solve these??

4. Yes but that would defy the point.

You can (must) use logarithms to solve question 1 as Pickslides shows.

2.) assume you are growing bacteria in a large petri dish. if you start with 10 g of bacteria growing exponentially at a rate of 10% per hour, then what is quantity of bacteria at the end of 10 hours?
The general formula for exponential growth is $A(t) = A_0(1+n)^{t}$

where:
• $A(t)$ = Amount at time t
• $A_0$ = Amount at time 0
• n = growth rate
• t = time

In question 2 you have $A(10) = A(10)$, $A_0 = 10$, $n = 0.1$ and $t=10$

$A(10) = 10(1+0.1)^{10}$