Question

The function
D(t) = 43.1224(1.0475)^t. gives the number of master’s degrees, in thousands, conferred on women in the United States t years after 1960. Find the number of master’s degrees earned by women in 1984, in 2002, and in 2010. Then estimate the number of master’s degrees that will be earned by women in 2020.?When will the number of master’s degrees earned by women in the U.S. reach a million?

Answer 1

We have

D(t) = 43.1224(1.0475)^t where t is no. of years after 1960.

For the year 1984, t= 1984- 1960= 24

So,

no. of master's degrees earned by women= D(24)= 43.1224(1.0475)²⁴= 131.341 thousand

So, 131341 master's degrees earned by women in the year 1984.

For the year 2002, t= 2002- 1960= 42

So,

no. of master's degrees earned by women= D(42)= 43.1224(1.0475)⁴²= 302.811 thousand

So, 302811 master's degrees earned by women the year 2002.

For the year 2010, t= 2010- 1960= 50

So,

no. of master's degrees earned by women= D(50)= 43.1224(1.0475)⁵⁰= 438.939 thousand

So, 438939 master's degrees earned by women the year 2010.

For the year 2020, t= 2020- 1960= 60

So,

no. of master's degrees earned by women= D(60)= 43.1224(1.0475)⁶⁰= 698.144 thousand

So, 698144 master's degrees will be earned by women in the year 2020.

Also, we need to find t such that no. of master's degrees= 1 million

So, D(t) = 1000

43.1224(1.0475)^t= 1000

1.0475^t=23.189

t= log(23.189)/log(1.0475)

t= 67.74

So, In (1960+ 67.74) = 2027.74 = 2028 year number of master’s degrees earned by women in the U.S. reach a million.

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