Respuesta :
In the first part of the question, we need to create an equation that models the number of people that can be fed in a given year. To do so, we start with the statement that at the initial time t = 0, 500 people can be fed, and combine it with the statement that the resources expand to feed 30 additional people every year. If we multiply the number of years ( T ) by 30, it will give the number of people that the additional resources will be able to feed. If we add it to the initial capacity, we have that moment's total capacity.
From the solution developed above, we are able to answer the first part of the question:
a)
[tex]P_{feed}=500+30*t[/tex]where t is the number of years after the beginning.
For the second part of the question, we need to remember that the calculation of X percent of a quantity consists of multiplying the given quantity by X and dividing it by 100. In the present problem, it is 5 percent of 500, which means it is 5*500 / 100, which results in 25. For the next year, the total population to be increased by 5% will not be the 500, but 525, and for this reason, we calculate the 5% as 5*525/100, and so on.
It means that, if we want to increase an amount by 5%, the multiplication to be done is by 1.05, which means that the consecutive increase is just an exponent of this 1.05 to be multiplied by the initial population. And from this, we are able to write the equation that models the number of people in a given year as follows:
b)
[tex]P_{population}=500*(1.05)^t[/tex]where t denotes the time in years passed from the begginning of the times.
