Continuous Exponential Growth: Final Value
How to find the final value of continuous exponential growth: formula, 1 example, and its solution.
The initial value of the weight is 10g.
So A0 = 10g.
The weight increases at a rate of 3% per second.
So r = 0.03/second.
Write the unit [per second].
The final value is the weight 1 [minute] later.
But the unit of the rate is [per second].
So write 1 minute in [seconds]:
t = 60 seconds.
A0 = 10
r = 0.03
t = 60
The weight increases continuously.
Then the expected weight A is
A = 10⋅e0.03⋅60.
0.03⋅60 = 1.8
assume e1.8 = 6.05.
So 10⋅e1.8 = 10⋅6.05.
10⋅6.05 = 60.5
The initial value A0 is in g.
So the final value A is 60.5g.
So 60.5g is the answer.