Question

A town currently has a population of 1,000,000, and the population is increasing 6 percent every year

a) using standard function notation , next = nowx1.06, starting at 1,000,000 use p to denote current population, r for the rate of population growth, and t for the number of years explain answer
b)is the function you wrote in the previous task recursive or non recursive?
c)compare the benefits of representing a situation using a recursive function versus using a regular function

Answer 1

a)
`1,000,000 * (1.06)^(t)`

b) The function is recursive

c) The benefits includes;

1) Simplification of information

2) Faster data access

3) Lesser storage requirement

4) Good for forecasting

5) Simplifies information analysis.

Explanation:

The given information are;

The current population = 1,000,000

The rate of increase of the population = 6%

a) With the standard function notation is
`P_f` =
`P_p` ×
`(1 + r)^(t)`

Where;

`P_f` = Future population

`P_p` = Present population

r = Rate of population increase

t = The number of years

Therefore, we have;

`P_f` = 1,000,000 ×
`(1 + 0.06)^(t)` = 1,000,000 ×
`(1.06)^(t)`

The population increases by a factor of
`(1.06)^(t)` given the number of years, t

b) The function is recursive as it takes account of the number of years and the previous population to calculate the future population

c) The benefits includes;

1) Simplification of the relationship of a given data with time

2) Provides a more faster way to access data that is recursive than using complex regular function with more variables

3) Reduces data storage space for statistical calculations as several particular data can be accessed using one function

4) Provides improved forecasting

5) Enables detailed information analysis.