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
2 answers:
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
where is the initial number of goats and <em>b</em> is the per capita growth rate.
From the question,
<em>b</em> = 0.5 <em>N</em> = 1000
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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