Use the data for 1960 and 2012 to find the value of k and to write an exponentia

Question

Use the data for 1960 and 2012 to find the value of k and to write an exponential function that describes the percent of adults married after time t, in years, where t is the number of years after 1960.

5.6.13 The data in the table shows that the percentage of adults in aYear Percent of Adults country who are currently married is declining. Assuming that the percentage of adults who are married will continue to decrease according to the exponential decay model: Complete parts a) through c) below. 1960 1980 2000 2010 2012 Who Are Married 65.4 55.2 50.2 44.6 42.4 a) Use the data for 1960 and 2012 to find the value of k. k=[ ] (Simplify your answer. Round to four decimal places as needed.)

Explanation / Answer

1960 = 65.4

2012 = 42.4

let 1960 = t = 0

2012 = t = 52

setting up the equation

65.4 = ae^0k

a = 65.4

42.4 = 65.4 e^(52k )

k = - 0.0083

b) percent of adults in 2015

= 65.4 e^ -.0083(55)

= 41.4

in 2018

= 65.4 e^ -.0083(58)

= 40.4

c) 40 = 65.4 e^ -.0083(t)

40 / 65.4 = e^-.0083t

t = 59 .23

so, the percent will be 40% in the year 2019

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