Question

The number of women graduating from​ 4-yr colleges in a particular country grew from 1930​, when 48,833 women earned a​ bachelor's degree, to 2004​, when approximately 870,000 women received such a degree. Find an exponential function that fits the​ data, and the exponential growth rate.

Answer 1

Answer:

$A(t) = 48833e^{0.0389t}$

The exponential growth rate is r = 0.0389

Step-by-step explanation:

An exponential function for the number of women graduating from​ 4-yr colleges in t years after 1930 can be given by the following equation:

$A(t) = A(0)e^{rt}$

In which A(0) is the initial amount, and r is the exponential growth rate, as a decimal.

1930​, when 48,833 women earned a​ bachelor's degree

This means that $A(0) = 48833$

2004​, when approximately 870,000

2004 is 74 years after 1930, which means that $A(74) = 870000$

Applying to the equation:

$A(t) = A(0)e^{rt}$

$870000 = 48833e^{74r}$

$e^{74r} = \frac{870000}{48833}$

$\ln{e^{74r}} = \ln{\frac{870000}{48833}}$

$74r = \ln{\frac{870000}{48833}}$

$r = \frac{\ln{\frac{870000}{48833}}}{74}$

$r = 0.0389$

So

$A(t) = A(0)e^{rt}$

$A(t) = 48833e^{0.0389t}$