AlinaMarieS
contestada

Each year, a group of 150 Alaskan wolves has an average birth rate of 15% and an average death rate of 37% per year. Which function could be used to predict when there will be 25 wolves in this group?

A. 150( (1.15)^t - (0.63)^t ) = 25
B. 150( (1.15)^t - (0.37)^t ) = 25
C. 150 (1.15 - 0.63)^t =25
D. 150 (1.15 - 0.37)^t =25

Respuesta :

nobillionaireNobley
Given that the starting population is 150 wolves, let the time when there will 25 wolves left be x, then
The increase in the number of wolves due to births is given by 150(1 + 0.15)^t = 150(1.15)^t
The decrease in the number of wolves due to dirths is given by 150(1 - 0.37)^t = 150(0.63)^t.
The number of wolves at time t is given by 150(1.15)^t - 150(0.63)^t = 150((1.15)^t - (0.63)^t).

Therefore, the function that could be used to predict when there will be 25 wolves in this group  is 150((1.15)^t - (0.63)^t) = 25. (option A).

The function that could be used to predict when there will be 25 wolves in this group is [tex]150(1.15^t - 0.63^t) = 25[/tex].

What is Percentage?

A percentage is a way to describe a part of a whole. such as the fraction 1/4 can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

We know that a 15% birth rate means that the number of wolves will increase by 15%, after every time period t, while the death rate represents that the number of wolves will decrease by 37% after t period of time.

Now, it is given that the birthrate will increase from the initial number(150) of wolves by 15%, therefore, we can represent the given situation by,

[tex]150(1+0.15)^t\\\\= 150(1.15)^t[/tex]

Also, the death will reduce the initial number(150) of wolves by 37%, therefore, the equation that may represent this will be,

[tex]150(1-0.37)^t\\\\= 150(0.63)^t[/tex]

Further, since both the situation are making changes in the number of wolves, therefore, we will substitute both the equation together, but also one situation is reducing the number of wolves while the other equation is increasing the number of wolves, therefore, the difference of the two-equation will give us the desired number of wolves,

[tex]150(1.15)^t - 150(1.15)^t[/tex]

taking 150 as common,

[tex]=150[(1.15)^t - (0.63)^t][/tex]

Hence, the function that could be used to predict when there will be 25 wolves in this group is [tex]150(1.15^t - 0.63^t) = 25[/tex].

Learn more about Percentage:

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