Answer:
a) ![M(t)=24000-14000e^{t/10}](https://tex.z-dn.net/?f=M%28t%29%3D24000-14000e%5E%7Bt%2F10%7D)
b) It takes 5.390 years to pay off the loan.
Step-by-step explanation:
(a) The differential equation for the variation in the amount of the loan M is
![\frac{dM}{dt}=0.1M-2400](https://tex.z-dn.net/?f=%5Cfrac%7BdM%7D%7Bdt%7D%3D0.1M-2400)
We can express this equation as:
![\frac{dM}{dt}=0.1M-2400\\\\10\int \frac{dM}{M-24000} =\int dt\\\\10ln(M-24000)=t\\\\M-24000=Ce^{t/10}\\\\M=Ce^{t/10}+24000\\\\M(0)=Ce^{0/10}+24000=10000\\\\C+24000=10000\\\\C=-14000\\\\M(t)=24000-14000e^{t/10}](https://tex.z-dn.net/?f=%5Cfrac%7BdM%7D%7Bdt%7D%3D0.1M-2400%5C%5C%5C%5C10%5Cint%20%5Cfrac%7BdM%7D%7BM-24000%7D%20%3D%5Cint%20dt%5C%5C%5C%5C10ln%28M-24000%29%3Dt%5C%5C%5C%5CM-24000%3DCe%5E%7Bt%2F10%7D%5C%5C%5C%5CM%3DCe%5E%7Bt%2F10%7D%2B24000%5C%5C%5C%5CM%280%29%3DCe%5E%7B0%2F10%7D%2B24000%3D10000%5C%5C%5C%5CC%2B24000%3D10000%5C%5C%5C%5CC%3D-14000%5C%5C%5C%5CM%28t%29%3D24000-14000e%5E%7Bt%2F10%7D)
(b) We can calculate this as M(t)=0
![M(t)=24000-14000e^{t/10}=0\\\\e^{t/10}=24000/14000=1.714\\\\t=10ln(1.714)=10* 0.5390=5.390](https://tex.z-dn.net/?f=M%28t%29%3D24000-14000e%5E%7Bt%2F10%7D%3D0%5C%5C%5C%5Ce%5E%7Bt%2F10%7D%3D24000%2F14000%3D1.714%5C%5C%5C%5Ct%3D10ln%281.714%29%3D10%2A%200.5390%3D5.390)
It takes 5.390 years to pay off the loan.
the answer should be C. 5.27
Answer:
Net money earned = $ 1537
Step-by-step explanation:
Wage for assembling motorcycle = $125
Number of motor cycles assembled last week = 11
Total money earned = $125 x 11 = $1375
Total payment for test ride $18
Number of motor cycles given for test ride last week = 9
Total money earned in test rides = $18 x 9 = $162
Hence, net money earned last week by Roger= $1375+$162 = $1537
Answer: B. z-311+311=151+311
Step-by-step explanation:
You do the opposite since you want to get rid of 311