In the second half of the 20th century, the city of Phoenix, Arizona exploded in
ID: 3016760 • Letter: I
Question
In the second half of the 20th century, the city of Phoenix, Arizona exploded in size. Between 1990 and 2000 the population of Phoenix increased exponentially. In 1990 the population was 0.92 million people and in 2000 the population was 1.231 million people. a. What is the 10-year growth factor? (1.231/0.92) b. Define an exponential function, f, to determine the population P in Phoenix (in millions of people) where the input values, t, represent the number of years since 1990. f(t)=0.92*e^(-2.0114t) c. Use the function you defined in part (b) to answer the following questions. i. Use function notation to represent the population in Phoenix (in millions of people) in 1993. 0.92*e^(-2.0114(3)) ii. Use function notation to represent the population in Phoenix (in millions of people) in 1992. 0.92*e^(-2.0114(2)) iii. Use function notation to represent the population in Phoenix (in millions of people) in 1997. [0.92*e^(-2.0114(7)) d. Use the function you defined in part (b) to predict in what year the population of Phoenix reached 1.15 million people. 58949Explanation / Answer
let 1990 = x= 0
2010 = x= 10
so we have two points ( 0 , 0.92 )
and ( 10 , 1.231 )
10 year growth factor = 1.231 / 0.92 = 1.3380
growth rate = 1 - 1.3380 = 0.3380
b) exponential function is
y = ab^t
1.231 = 0.92 (b)^10
b^10 = 1.3380434
b = 1.029549
function is
f(t) = 0.92 (1.029549)^t
c) population in 1993 is plug t = 3
y = 0.92 (1.029549)^3
y = 1.004 million
ii) population in 1992 is plug t = 2
y = 0.975 million
iii) population in 1997 is plug t = 7
y = 1.128 million
d) plugging y = 1.15 and solving for x
y = 0.92 (1.029549)^x
1.15 = 0.92 (1.029549)^x
ln 1.15/0.92 = x ln 1.029549
x = 7.66
therefore in 1998 approximately population of phoenix reached 1.15 million