on an island without squirrels some squirrels are introduced. a mathematical model of the population growth of squirrels on the island is given by the function f defined by
f(x)= 1320/(1 + e^(5,1-0.66x))
where x is the time in years after the introduction
a)how many squirrels were introduced in the island?
b) how many squirrels are living on the island after 6 years
Thanks a lot
a) 1320 squirrels because there are no variables next to it(it is a constant)
I am going to assume that you are using a comma instead of the North American period to indicated the decimal place, so I will read that as:
f(x)= 1320/(1 + e^(5.1 - 0.66x)) ,
(why are you using the comma in the first number and then the period in 0.66 ??)
so at introduction, x = 0
and
f(0) = 1320/( 1 + e^5.1) = appr 8
after 6 years,
f(6) = 1320/(1 + e^(5.1 - .66(6))
= ....
you do the button-pushing
jj
To answer these questions, we need to evaluate the function f(x) at certain values of x.
a) To find out how many squirrels were introduced to the island, we need to determine the initial population. In this case, the initial population is represented by f(0), as x = 0 represents the time when the squirrels were introduced. Let's calculate it:
f(0) = 1320 / (1 + e^(5.1 - 0.66 * 0))
Since any number raised to the power of 0 is equal to 1, the exponential term simplifies to:
e^(5.1 - 0.66 * 0) = e^5.1
To find the value of e^(5.1), you can use a scientific calculator or any other relevant tool. Approximating it, we get:
e^(5.1) ≈ 164.07
Substituting this value back into the equation:
f(0) = 1320 / (1 + 164.07)
f(0) ≈ 1320 / 165.07 ≈ 7.9995
Therefore, approximately 8 squirrels were introduced to the island.
b) To determine the number of squirrels on the island after 6 years, we need to evaluate f(6). Let's calculate it:
f(6) = 1320 / (1 + e^(5.1 - 0.66 * 6))
Simplifying further:
e^(5.1 - 0.66 * 6) = e^1.26
Approximately, e^(1.26) ≈ 3.520
Substituting this value back into the equation:
f(6) = 1320 / (1 + 3.520)
f(6) ≈ 1320 / 4.520 ≈ 292.0355
Therefore, approximately 292 squirrels will be living on the island after 6 years.
Please keep in mind that these calculations are approximations and may vary slightly depending on the precision of the values used.