Answer:
13
Step-by-step explanation:
Sorry i cannot showy solution
Answer:
234 in^2
Step-by-step explanation:
*look at the pick* 6+60+168=234
Answer:
A. ![\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%3D2%7D%3D644.15%7D)
B. ![\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%20%3D%205.79%7D%3D%20839.86%20%7D)
Step-by-step explanation:
Given that:
An investment of Amount = $8000
earns at an annual rate of interest = 7% = 0.07 compounded continuously
The objective is to :
A) Find the instantaneous rate of change of the amount in the account after 2 year(s).
we all know that:
![A = Pe^{rt}](https://tex.z-dn.net/?f=A%20%3D%20Pe%5E%7Brt%7D)
where;
![A = (8000) \ e ^{0.7t}](https://tex.z-dn.net/?f=A%20%3D%20%288000%29%20%5C%20e%20%5E%7B0.7t%7D)
The instantaneous rate of change = ![\dfrac{dA}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D)
![\dfrac{dA}{dt} = \dfrac{d}{dt}(8000 \ e ^{0.07t} )](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%20%3D%20%5Cdfrac%7Bd%7D%7Bdt%7D%288000%20%5C%20e%20%5E%7B0.07t%7D%20%29)
![= 8000 \dfrac{d}{dt}e^{0.07 \ t}](https://tex.z-dn.net/?f=%3D%208000%20%5Cdfrac%7Bd%7D%7Bdt%7De%5E%7B0.07%20%5C%20t%7D)
![\dfrac{dA}{dt}= 8000 (0.07)e^{0.07 \ t}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%3D%208000%20%280.07%29e%5E%7B0.07%20%5C%20t%7D)
![\dfrac{dA}{dt}= 560 e^{0.07 \ t}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%3D%20560%20e%5E%7B0.07%20%5C%20t%7D)
At t = 2 years; the instantaneous rate of change is:
![\dfrac{dA}{dt}|_{t=2}= 560 e^{0.07 \times 2}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%3D2%7D%3D%20560%20e%5E%7B0.07%20%5Ctimes%202%7D)
![\mathtt{\dfrac{dA}{dt}|_{t=2}=644.15}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%3D2%7D%3D644.15%7D)
(B) Find the instantaneous rate of change of the amount in the account at the time the amount is equal to $12,000.
Here the amount = 12000
![12000 = (8000)e^{0.07 \ t}](https://tex.z-dn.net/?f=12000%20%3D%20%288000%29e%5E%7B0.07%20%5C%20t%7D)
![\dfrac{12000 }{8000}= e^{0.07 \ t}](https://tex.z-dn.net/?f=%5Cdfrac%7B12000%20%7D%7B8000%7D%3D%20e%5E%7B0.07%20%5C%20t%7D)
![1.5= e^{0.07 \ t}](https://tex.z-dn.net/?f=1.5%3D%20e%5E%7B0.07%20%5C%20t%7D)
㏑(1.5) = 0.07 t
0.405465 = 0.07 t
t = 0.405465 /0.07
t = 5.79
![\dfrac{dA}{dt}= 560 e^{0.07 \ t}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%3D%20560%20e%5E%7B0.07%20%5C%20t%7D)
At t = 5.79
![\dfrac{dA}{dt}|_{t = 5.79}= 560 e^{0.07 \times 5.79}](https://tex.z-dn.net/?f=%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%20%3D%205.79%7D%3D%20560%20e%5E%7B0.07%20%5Ctimes%205.79%7D)
![\mathtt{\dfrac{dA}{dt}|_{t = 5.79}= 839.86 }](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cdfrac%7BdA%7D%7Bdt%7D%7C_%7Bt%20%3D%205.79%7D%3D%20839.86%20%7D)
Answer:
45 is the anwser
Step-by-step explanation:
thank you
Answer:
Step-by-step explanation: