Chapter 4

Question 1

Exponential Function

Answer 1

f(x) = bˣ

Question 2

Power Function

Answer 2

g(x) = x³

Question 3

Compound Interest

Answer 3

A(t) = P(1+r/n)ⁿᵗ

Question 4

A(t)

Answer 4

Amount after t years

Question 5

P

Answer 5

Principal

Question 6

APY (Annual Percentage Yield)

Answer 6

(1+r/n)ⁿ

Question 7

Continuous Compound Interest

Answer 7

A(t) = Peʳᵗ

Question 8

Log Function

Answer 8

log(x) = (10ˡᵒᵍ⁽ˣ⁾)

Question 9

Natural Log Function

Answer 9

ln(x) = logₑˣ(x)

Question 10

No Subscript?

Answer 10

Take 10 To Each Side

Question 11

Undefined

Answer 11

ln ≤ 0

Question 12

Log Law 1

Answer 12

log(AB) = logA + logB

Question 13

Log Law 2

Answer 13

log(A/B) = logA - logB

Question 14

Log Law 3

Answer 14

logAᶜ = C(log)A

Question 15

Special Product 1

Answer 15

(A+B)² = A²+2AB+B²

Question 16

Special Product 2

Answer 16

(A-B)² = A²-2AB+B²

Question 17

Special Product 3

Answer 17

(A-B)(A+B)=A²-B²

Question 18

Initial Amount + Doubling Time

Answer 18

n(t) = n₀(2ᵗ/ᵈ)

Question 19

Common Mistake 1

Answer 19

log(A+B) = logA + logB

Question 20

Common Mistake 2

Answer 20

log(A-B) = logA - logB

Question 21

Common Mistake 3

Answer 21

log(A/B) = logA/logB

Question 22

Common Mistake 4

Answer 22

log¹⁰/log² = log⁵

Question 23

Common Mistake 5

Answer 23

ln(x)⁷ = 7(ln)x

Question 24

Non-Linear Equalities (Sign Chart) Step 1

Answer 24

Get 0 on one side.

Question 25

Non-Linear Equalities (Sign Chart) Step 2

Answer 25

Factor other side.

Question 26

Non-Linear Equalities (Sign Chart) Step 3

Answer 26

Find where top or bottom is equal to 0 and break x-axis at this point.

Question 27

Non-Linear Equalities (Sign Chart) Step 4

Answer 27

Sample the signs of the factors in each interval.

Question 28

Non-Linear Equalities (Sign Chart) Step 5

Answer 28

Tally the signs.

Question 29

Non-Linear Equalities (Sign Chart) Step 6

Answer 29

Give the interval.