# Math Help - Differential equation problem

1. ## 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?

2. ## Re: Differential equation problem

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:

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