Respuesta :
Answer:
a) [tex]\frac{dA}{dt}=400 e^{0.08(1)} =433.315[/tex]
b) [tex]\frac{dA}{dt}=400 e^{0.08(10)} =890.216[/tex]
c) [tex]\frac{dA}{dt}=400 e^{0.08(50)} =21839.260[/tex]
Step-by-step explanation:
For this case we have the following expression for the balance:
[tex] A = 5000 e^{0.08t}[/tex]
And we are interested on the rate at which the balance is changing for some values of t. The correct way to answer this is finding the derivate respect to t of A like this:
[tex]\frac{dA}{dt}= \frac{d}{dt} (5000 e^{0.08t})[/tex]
[tex]\frac{dA}{dt}= 5000 \frac{d}{dt}(e^{0.08t})[/tex]
[tex]\frac{dA}{dt}= 5000*0.08 e^{0.08t}[/tex]
[tex]\frac{dA}{dt}=400 e^{0.08t}[/tex]
So then we can solve for the different years like this
Part a
t= 1 years
[tex]\frac{dA}{dt}=400 e^{0.08(1)} =433.315[/tex]
So on this case would be $433.315 dollars per year
Part b
t=10 years
[tex]\frac{dA}{dt}=400 e^{0.08(10)} =890.216[/tex]
So on this case would be $890.216 dollars per year
Part c
t=50 years
[tex]\frac{dA}{dt}=400 e^{0.08(50)} =21839.260[/tex]
So on this case would be $21839.260 dollars per year
