Question

b) The number of ants in an colony increases exponentially at a rate of 4.6% per week. How long do you have to wait until the ant colony has tripled in size?

Answer 1

x(1+0.046)^n = 3x

Answer 2

FInd n

Answer 3

gimme a sec

Answer 4

The concept is after 1 week, the size of ant colony will be
x + 4.6% of x = x(1+0.046)

Answer 5

Let x(1+1.046) = y
In the second week again it will become
y + 4.6% of y = y(1+0.046) = x(1+0.046)(1+0.046) = x(1+0.046)^2

Answer 6

and so on

Answer 7

well I'd use

\[P_{n} = P_{0} \times e^kt\]

and for the population to triple

\[P_{0} = 1 ... and..... P_{n} = 3\]

so the equation becomes

\[3 = 4^{0.046 \times t}\]

hopefully that helps you solve for the time...

Answer 8

After n weeks -> x(1+0.046)^n which should be equal to 3x

Answer 9

oops the equation should read

\[3 = e^{0.046\times t}\]

solve for t

Answer 10

@cambell_st : I don't think exponential growth means what you think
http://en.wikipedia.org/wiki/Exponential_growth

Answer 11

@campbell_st

Answer 12

not to be confused with e being called an exponential function

Answer 13

well if you use the phrase exponential growth you need a base and exponent...

I found it would take approx 24 weeks

and using the compound interest formula as you have done... which is also a growth model...

the time is 24.4.... so rounding.... or approx 24 weeks...

ummm... which is correct...

Answer 14

and here is a site that talks about growth and decay in terms of e

http://www.mathsisfun.com/algebra/exponential-growth.html

Answer 15

the only determining factor is whether you are told that the rate of growth is proportional to itself...

so who knows

Answer 16

i get your viewpoint now
i used the above form of exponential growth because the growth is mentioned in percentage

Answer 17

*growth rate