Domain = x<18000(You cant og a negative number)
Am I actually supposed to graph it? enter the equation on desmos.com
It takes longer to make the same altitudinal gain
t=50log(18000/(18000-4000))=50log(18000/14000)=5.457
Annuities whose payments are made at the end of the period are "ordinary annuity" type
![\bf \qquad \qquad \textit{Future Value of an ordinary annuity} \\\\ A=pymnt\left[ \cfrac{\left( 1+\frac{r}{n} \right)^{nt}-1}{\frac{r}{n}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%5Cqquad%20%5Ctextit%7BFuture%20Value%20of%20an%20ordinary%20annuity%7D%0A%5C%5C%5C%5C%0AA%3Dpymnt%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7Br%7D%7Bn%7D%20%5Cright%29%5E%7Bnt%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%20%5Cright%5D)
![\bf \qquad \begin{cases} A= \begin{array}{llll} \textit{accumulated amount} \end{array} \\ pymnt=\textit{periodic payments}\to &100\\ r=rate\to 14\%\to \frac{14}{100}\to &0.14\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus} \end{array}\to &52\\ t=years\to &5 \end{cases} \\\\\\ A=100\left[ \cfrac{\left( 1+\frac{0.14}{52} \right)^{52\cdot 5}-1}{\frac{0.14}{52}} \right]](https://tex.z-dn.net/?f=%5Cbf%20%5Cqquad%20%0A%5Cbegin%7Bcases%7D%0AA%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Baccumulated%20amount%7D%0A%5Cend%7Barray%7D%0A%5C%5C%0Apymnt%3D%5Ctextit%7Bperiodic%20payments%7D%5Cto%20%26100%5C%5C%0Ar%3Drate%5Cto%2014%5C%25%5Cto%20%5Cfrac%7B14%7D%7B100%7D%5Cto%20%260.14%5C%5C%0An%3D%0A%5Cbegin%7Barray%7D%7Bllll%7D%0A%5Ctextit%7Btimes%20it%20compounds%20per%20year%7D%5C%5C%0A%5Ctextit%7Bweekly%2C%20thus%7D%0A%5Cend%7Barray%7D%5Cto%20%2652%5C%5C%0At%3Dyears%5Cto%20%265%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0AA%3D100%5Cleft%5B%20%5Ccfrac%7B%5Cleft%28%201%2B%5Cfrac%7B0.14%7D%7B52%7D%20%5Cright%29%5E%7B52%5Ccdot%205%7D-1%7D%7B%5Cfrac%7B0.14%7D%7B52%7D%7D%20%5Cright%5D)
18% of 20000 = 3600(0.18 x 20000 = 3600)
3600 x 4 years = 14400
(original value - depreciated value in 4 years: 20000 - 14400 = 5600)
The current value of the car is at £5600
