6, Social scientists are modeling the US. population. The scientist use the mode

Question

6, Social scientists are modeling the US. population. The scientist use the model y = Pert (6.1) (8 points) Find the the rate of growth, r, since 1980 using this information: in 1980 the U.S population was 227 million and in 2000 it was 281 million exact value of r = 6.2) (2 points) Use a calculator to approximate your answer in (6.1). Write the rate as a percentage rounded to two decimal places. approximate value of r, given as a percentage: --% (6.3) (8 points) Based on the rate from (6.1), how long will it take for the US population to double? Give an exact answer (using the exact rate from 2.1) exact doubling time: 6.4) (2 points) Use a calculator to approximate your answer in (6.3) Write the answer rounded to the nearest year.

Explanation / Answer

1) 1980 population = 227 million

in 2000 = 281 million

we have two points ( 0, 227 ) , ( 20 , 281 )

plugging the points in the equation

y = pe^rt

227 = pe^0

p = 227

281 = 227e^20r

281 / 227 = e^20r

ln 281 / 227 = 20r

r = ln (281/227) / 20

2) rate of percentage = 1.05%

3) ln 2 = e^ ln (281/227) / 20 t

t = ln 2 / ln (281/227) / 20

4) rounded to nearest year 1980 + 14

year = 1994

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

---

---

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