5.5--Bases Other Than e
Compound Interest Formula:
A = P (1 +
r
n
nt
)
P = principal
r = rate of interest
Continuously Compounded
Interest Formula:
A = Pert
1)
t = time (usually in years)
n = # of times compounded
per year
Jared saw a used car the other day for $3200.
Unfortunately, he only has $2855 saved up. If he
deposits this money into a bank paying 3.5% interest
compounded monthly, how long will it take him to earn
enough interest to afford the car?
1
5.5--Bases Other Than e
2)
A certain amount of money is in a savings account
earning 4.5% interest, compounded quarterly.
How long will it take this money to double in value?
3)
A certain amount of money is in a savings account
earning 4.5% interest, compounded continuously.
How long will it take this money to double in value?
e ≈ 2.71828182845904523
2
5.5--Bases Other Than e
The derivative of ax:
(a is a positive constant.)
If y = ax, then dy/dx = ax
ln a
Find dy/dx:
4)
y = 6x
7)
y = 1x
5)
y = 17x
8)
6)
y = 25x
y = ex
Find dy/dx:
9)
y = 53x-4
10)
y = 9tan 2x
3
5.5--Bases Other Than e
If y = ax, then dy/dx = ax
ln a
Find dy/dx:
11)
12)
y = 3x (112x+7)
y = log
7
x3 - 5
4
5.5--Bases Other Than e
Find dy/dx using logarithmic differentiation:
y = x3x-4
13)
14)
y = xtan 2x
The integral of ax...
x
If f(x) = a , then
ax
f(x) dx =
ln a
+ C
Integrate:
15)
17)
8x dx
16)
(10x4 + 53x-1) dx
41tan x dx
1 - sin2x
5
5.5--Bases Other Than e
If f(x) = ax, then
f(x) dx =
ax
ln a
+ C
From our textbook, p. 369
Find the antiderivative:
3 2x
1 + 3 2x
81)
dx
2
2x dx
83)
-1
6