Expo, Log, Cubic, Poly Func Practice Problems

Question 1

A biologist predicts that the height of a certain tree will increase exponentially with time, tripling every 60 years. The tree is now 5 meters tall. According to the biologist’s prediction, in how many years would the tree become 45 meters tall?

Answer 1

120 years

Question 2

Technetium-99m is used by doctors on patients when needing to x-ray and track organ function. It has a half-life of approximately 6 hours. If a patient is given 1000 mg for a procedure, in how many hours will 62.5 mg of Technetium-99m remain in the bloodstream?

Answer 2

24 hours

Question 3

Mr. Sanchez invested $5000 in a college fund for his daughter. The college fund earns interest at an annual rate of 5%, compounded monthly. Approximately how much money will be in the fund in 15 years, if Mr. Sanchez does not make any deposits or withdrawals?

Answer 3

10,568.52 dollars

Question 4

Describe the transformation of this function: f(x) = -3^(x - 2) + 4

Answer 4

Reflection off x axis
Right 2
Up 4
Vertically Compressed by a factor of 3

Question 5

Describe the transformations of this function: f(x) = log(x + 5) - 6

Answer 5

Left 5
Down 6

Question 6

Solve for x: 50(2)^x = 250

Answer 6

x=2.32

Question 7

log(3x) = 5

Answer 7

33,333.33

Question 8

f(x) = (x + 2)(x + 1)(x - 1)(x - 2)

State the interval(s) where f(x) > 0

Answer 8

(-∞, -2)
(-1, 1)
(2, ∞)

Question 9

f(x) = (x + 2)(x + 1)(x - 1)(x - 2)

State the interval(s) where f(x) is increasing

Answer 9

(-1.58114, 0)
(1.58114, +∞)

Question 10

f(x) = (x + 2)(x + 1)(x - 1)(x - 2)

Describe the end behaviors.

Answer 10

As x->+∞ f(x) ->+∞
As x->-∞ f(x) -> +∞

Question 11

f(x) = (x + 2)(x + 1)(x - 1)(x - 2)

State the Domain and Range.

Answer 11

Domain: ℝ
Range: [-2.25, +∞)

Question 12

A polynomial, P(x), has a leading coefficient of 1 and exactly three distinct zeros.
x = -1 is a zero of multiplicity two
x = 2 is a zero of multiplicity one
x = 4 is a zero of multiplicity one

Write the factored form of P(x).

Answer 12

P(x)=(x+1^)2(x-2)(x-4)

Question 13

A polynomial, P(x), has a leading coefficient of 1 and exactly three distinct zeros.
x = -1 is a zero of multiplicity two
x = 2 is a zero of multiplicity one
x = 4 is a zero of multiplicity one

Write the standard form of P(x).

Answer 13

P(x)=x^4-4x^3-3x^2+10x+8