Some scientists estimate the growth of a population using the Malthusian model, named after the Reverend Thomas Malthus, who wrote one of the most influential books on population. His formula uses the natural logarithm, which you will learn about in a future lesson.
Another formula that models growth is shown, where No is the initial size of the population, N is the final size of the population, r is the rate of growth or decay per time period, and t is the number of time periods. In this case, r = 100% or 1. Using this formula, how many rabbits would Daisy have after 3 years?
N =No(1 + r)t

Question

Some scientists estimate the growth of a population using the Malthusian model, named after the Reverend Thomas Malthus, who wrote one of the most influential books on population. His formula uses the natural logarithm, which you will learn about in a future lesson.
Another formula that models growth is shown, where No is the initial size of the population, N is the final size of the population, r is the rate of growth or decay per time period, and t is the number of time periods. In this case, r = 100% or 1. Using this formula, how many rabbits would Daisy have after 3 years?
N =No(1 + r)t

anonymous · Answer

i came out with 16384

anonymous · Answer

@amistre64

anonymous · Answer

@sammixboo

amistre64 · Answer

No is the initial size of the population, 
  N is the final size of the population, 
     r is the rate of growth or decay per time period, and 
          t is the number of time periods. 

In this case, r = 1. Using this formula, how many rabbits would Daisy have after 3 years?
N =No(1 + r)t

whats the initial population count, 2 maybe?

amistre64 · Answer

is 3 years broken into smaller periods?  or does 1 year measure 1 period?

anonymous · Answer

(Hints: Remember that your starting number is 2. The exponent is determined by the number of periods of doubling. Use your calculator.)

anonymous · Answer

sorry forgot to post the first problem

anonymous · Answer

Daisy purchased a rabbit couple to keep as pets. Perhaps Daisy got more than she bargained for! If the population of rabbits doubles every 3 months, how many rabbits will Daisy have at the end of 3 years? (Hints: Remember that your starting number is 2. The exponent is determined by the number of periods of doubling. Use your calculator.)

anonymous · Answer

my answer was 8192

anonymous · Answer

not sure if that helps the 2nd problem alludes me completely lol.

amistre64 · Answer

N = 2(1+1)^3

so long as 1 year is 1 periodic rate.

spose they take 3 months to cycle thru 1 period,  4 periods per year is 12 periods in 3 years

N = 2(1+1)^12

anonymous · Answer

ok so N=8192?

amistre64 · Answer

doubles every 3 months gives us

n0 = 2
n1 = 2(2)
n2 = 2(2)(2)
n3 = 2^4

n_i = 2^{i-1}

amistre64 · Answer

2^11 = 2048

anonymous · Answer

mm you lost me

amistre64 · Answer

was making a geometric progression to make sure of something

anonymous · Answer

i plugged in N = 2(1+1)^12 and got N=8192

anonymous · Answer

oh ok

amistre64 · Answer

No = 2(1+1)^0
N1 = 2(2)^1
N2 = 2(2)^2
...
N12 = 2(2)^12 = 8192  yes

anonymous · Answer

thank you very much!

amistre64 · Answer

youre welcome