Unit 4&5

Exp. functions MC

100

2^3x+5= 128

a. x= 3/2
b. x= 8
c. x= 2.5
d. x= 2/3

d. x= 2/3

200

1000^x= (1/100)^4-x
a. x= -8
b. x= 6
c. x= 8
d. x= -6

a. x= -8

300

78= 401e^-0.02+11

107.19

400

log₃(2x+5)=2
a. x= 2
b. x= 4
c. x= 2.5
d. x= 3

a. x=2

Exp. functions SA

100

Are exponential functions one to one? How can you tell? What does this tell you about their inverses.

Yes, they pass the HLZ. Their inverse is also a function.

200

If a person invests $700 into an account and recieves a nominal rate of 8% continuously compounded, what would be the expression?

700e^0.08t

300

 500 = 1000e^{-.75 x}, What is x?

x= 0.9242

400

What is the equation if account K has $500 invested with an interest rate 5% per year?

500(1.05)^t

Series & Sequences MC

100

Determine an algebraic formula that defines the sequence:
5, 10, 15, 20

a. a(n)= n₅
b. a(n)= n+5
c. a(n)= 5_n
d. a(n)= 5n

d. a(n)= 5n

200

A recursive sequence is defined by a_n+1 = 2a_n-1 with a₁= 0 and a₂= 1. Which of the following represents the value of a₃?

a. 2
b. 4
c. 3
d. 5

a. 2

300

Which of the following formulas would represent the sequence 10, 20, 40, 80, 160...

a. a(n) = 2n
b. a(n) = n²
c. a(n) = 10(2)n
d. a(n) = 10(2)_n

c. a(n)= 10(2)n

400

Find the sum of the geometric series with the following properties: a₁= -5, r= -2 and n=10
a. 1,250
b. 1,705
c. 2,020
d. 790

b. 1,705

Series & Sequences SA

100

Determine an algebraic formula that defines the sequence:
3,9,27,81

a(n)= 3ⁿ

200

For the following sequence state a recursive definition. Be sure to include a starting value or values:
8,6,4,2

Each term is two less than the previous: a₁ =2 and a_n+1 = -1a_n

300

If the geometric series 54+36+...+128/27 has seven terms in its sum then the value of the sum is..

4118/27 or 152.6

400

Find the sum of the geometric series with the following properties:
a₁= 20, r= 1/2, and n=6

39,375

Random

100

Find the sum of the geometric series with the following properties:

a₁= 6, r= 3 and n=8

a. 19,680
b. 18,940
c. 20,280
d. 18,620

a. 19,680

200

Which of the following is not an exponential function?

1. f(x) = 3e-2 x
2. g(x) = 2x/2
3. h(x) = x3/2
4. g(x) = 15 / 7x

c. h(x)= x3/2

300

For the following sequence, state a recursive definition. Be sure to include a starting value or values:
2, -2, 2, -2

Each term is the previous term multiplied by -1:
a₁= 2 and a_n+1 = -1a_n

400

 Solve for x..  e^-2x= 27

x= -1.648