# Differential equation problem

• Jul 20th 2012, 10:53 PM
kethgr
Differential equation problem
One study suggests that from 1955 to 1970, the number of bachelor's degrees in physics awarded per year by U.S. universities grew exponentially, with growth constant k=0.089.
If exponential growth continues, how long will it take for the number of degrees awarded per year to increase 15-fold?
If 2000 degrees were awarded in 1955, in which year were 7500 degrees awarded?
• Jul 21st 2012, 02:16 AM
earboth
Re: Differential equation problem
Quote:

Originally Posted by kethgr
One study suggests that from 1955 to 1970, the number of bachelor's degrees in physics awarded per year by U.S. universities grew exponentially, with growth constant k=0.089.
If exponential growth continues, how long will it take for the number of degrees awarded per year to increase 15-fold?
If 2000 degrees were awarded in 1955, in which year were 7500 degrees awarded?

1. The general equation of exponential growth is:

$a(t) = a(0) \cdot e^{kt}$

where a(t) denotes the amount at time t, a(0) is then consequently the initial amount at t = 0.

2. If a(t) = 15a(0)

then you have to solve for t:

$15a(0) = a(0) \cdot e^{0.089 \cdot t}$

3. If the initial value is 2000 and the actual amount is 7500 you have to solve for t:

$7500=2000 \cdot e^{0.089 \cdot t}$