MATH SOLVE

3 months ago

Q:
# please help hulkk this ties with my last question.In the year 1995, the population of a town in Texas was recorded as 25,400 people. Each year since 1995, the population has increased on average by 11% each year.i. Write an exponential function to represent the town’s population, y, based on the number of years that pass, x after 1995. j. Explain the similarities and differences between your equations in Tasks 2 and 3.k. During what year will the population of the town in Task 3 first exceed that of the city in Task 2? Show all of your work and explain your steps.

Accepted Solution

A:

Answer:i. Write an exponential function to represent the town’s population, y, based on the number of years that pass, x after 1995.[tex]y=25400(1.11^{x})[/tex]j. Explain the similarities and differences between your equations in Tasks 2 and 3.SimilaritiesBoth functions are exponential in nature, owing to the fact that the independent variable is the exponent.DifferencesThe equation in task 2 represented an exponential decay model, where the population was declining over time, while the equation in task 3 is an exponential growth model since the number of people is increasing over the years.k.2019Step-by-step explanation:The initial population is given as 25,400 and the annual percentage increase is 11%. The annual growth factor will thus be;[tex](1+\frac{11}{100})=1.11[/tex]The exponential function will thus be;[tex]y=25400(1.11^{x})[/tex]To determine the year that the population of the town in Task 3 first exceed that of the city in Task 2 we simply graph both functions on the same graph. Find the attached;from the graph, we note that both towns will have the same number of people 23.9 years after 1995. Implying that 24 years after 1995 the population of the town in Task 3 will first exceed that of the city in Task 2. The respective year will be 1995+24 = 2019