[16 points] 4) The exponential function -2170.008) States (in millions of people

Question

[16 points] 4) The exponential function -2170.008) States (in millions of people) years after 1960. a) What was the population in 1960 (to the nearest million)? models the population of the United b) What is the current population (to the nearest million)? c) How much did the population increase from 1980 to 1990 (to the nearest million)? d) When is it predicated to hit 400 million? Show your work algebraically e) Draw a well-labelled graph covering the years 1950 to 2050 indicating the data points in parts a through d. Label each point with its x and y coordinates.

Explanation / Answer

Given

y = 217(1.008)x

(a) Population in 1960 = 217 million

(b) Consider current year 2017, x = 2017 – 1960 = 57 years

    y = 217*(1.008)^57 = 341.75 million

(c) Population in 1980, x = 20 years

     y = 217*(1.008)^20 = 254.5 million

     Population in 1990, x = 30 years

     y = 217*(1.008)^30 = 275.6 million

    Population increase = 275.6 – 254.5 = 21.1 million

(d) 400 = 217*(1.008)^x

       (1.008)^x = 400/217 = 1.843

         x = 76.75 years

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.