exponentials

Question 1

what are the components of an exponential equation ( Y=a^X

Answer 1

y = answer 
a = base 
X = power

Question 2

name these properties of the natural exponential ? Y=E^X

a. y axis intercept
b. asymptote
c. rational or irrational

Answer 2

a. y = 1
b. y = 0
c. irrational ( never able to be fully calculated )

Question 3

name some of the rules of E^x

Answer 3

e^0 = 1

e^a . e^b = e^a+b

e^a / e^b = e^a-b

1/e^a = e^-a

(e^a)^b = e^ab

Question 4

how do you calculate: (after n years, at R% interest, with original investment or loan £P)

how much you would have in your bank account or how much do you owe to the lender ?

Answer 4

total = P ( 1 + R/100 )^n

Question 5

how do you calculate compound interest total (Pt) after (t) years ?

Answer 5

Pt = P0 ( 1 + r/n ) ^ nt

Pt - total after t years
P0 - principal amount
r - interest rate per annum as a fraction not as a percentage
n - number of time interest is paid during the year
t - number of years

Question 6

as the frequency of compounding rises, the future value rises and approaches a fixed value. this value can be calculated directly. how do you do this ?

Answer 6

Pt = P0.e^rt

Question 7

what are the log rules ?

Answer 7

ln|1| = 0
ln|a| + ln|b| = ln|ab|
ln|a| - ln|b| = ln|a/b|
-ln|a| = ln|1/a|
ln|(a^b)| = bln|a|

Question 8

what is the derivative of :

a. d(e^x)/dx
b. d(e^f(x))/dx
c. d(ln|x|)/dx
d. d(ln|f(x)|)/dx

Answer 8

a. = e^x
b. = e^f(x) . f’(x)
c. = 1/x
d. = f’(x)/f(x)

Question 9

what is the derivative of y=a^x?

Answer 9

dy/dx = a^x . ln|a|

Question 10

what is the derivative of y=u.v.w ?

Answer 10

ln|y| = ln|u| . ln|v| . ln|w|

1/y.dy/dx=(1/u.du/dx).(1/v.dv/dx).(1/w.dw/dx)

BUT REALLY TO SOLVE THIS :

y = u.v

ln|y| = ln|u| . ln|v|

then to get dy/dx you must times the ln|u|.ln|v| by the original y