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xz_007 [3.2K]
3 years ago
14

g A sailing ship stopped at several islands, releasing one mating pair of goats onto each one. On the large island, the goats' g

rowth rate was approximately exponential for a long time. If their per capita growth rate is 0.5 per year, how many years will it take before the goat population reaches 1000
Mathematics
2 answers:
PSYCHO15rus [73]3 years ago
5 0

Answer:

The goat population reaches 1000 in 12.4 years

Step-by-step explanation:

After <em>t </em>years, the number of goats is given by

N = N_0e^{bt}

where N_0 is the initial number of goats and <em>b</em> is the per capita growth rate.

From the question,

  • N_0 = 2
  • <em>b</em> = 0.5
  • <em>N</em> = 1000

1000 = 2e^{0.5t}

e^{0.5t} = 500

0.5t = \ln 500 = 6.214

t = \dfrac{6.2}{0.5} = 12.4

Serggg [28]3 years ago
4 0

Answer:

12.4 years  

Step-by-step explanation:

Let recall the following,

The number of goats after t years is shown below

N = N₀∧ebt

Let N₀ = the number of the initial goats

b = The capital rate of growth

From the example given,

Let insert the values

N₀ is = 2

b = 0.5

Let N = 1000

So,

1000= 2e∧0.5t

e∧0.5t = 500

0.5t = ln 500 = 6.214

Therefore

t = 6.214/0.5 =12.4

Therefore, the number of years it will take for the goat population to reach 1000 is = 12.4 years  

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