Logarithmic Functions Problems

Question 1

What is the domain of f\left(x\right)=\log_4x?

Accepted Answer

x > 0

Question 2

You are allowed to talk with your teammates ("confer") on what kind of quiz bowl questions..

Accepted Answer

Bonus questions, but not toss-up questions

Question 3

If C\left(h\right)=120\left(0.5\right)^{\frac{h}{4}} how many hours will it take for only 60mg of caffeine to remain?

Accepted Answer

4 hours

Question 4

If a premium's monthly cost can be modelled as y=2.1\left(1.0755\right)^x, how much would a person age 65 pay?

Accepted Answer

2.1\left(1.0755\right)^{65}=238.18

Question 5

What translations will take place in g\left(x\right)=\log_4\left(x+5\right)-3 compared to f\left(x\right)=\log_4x?

Accepted Answer

Left 5, Down 3

Question 6

True or false: When solving 5\log_48x^2=10, the first thing you should do is divide the equation by 5.

Accepted Answer

True

Question 7

What is the caffeine in Lindsey after 2 hours if the caffeine is modelled by C=120\left(0.5\right)^{\frac{h}{4}}?

Accepted Answer

84.853 mg

Question 8

When given y=a\cdot b^x and points (5,121.5) and (6,364.5), how do we find b?

Accepted Answer

Use 364.5 / 121.5 = 3

Question 9

If we can simplify a problem to 4^2=8x^2 what are valid values of x to solve the equation

Accepted Answer

x=\pm\sqrt{2}

Question 10

True or false: \log_93=kmeans 9^k=3.

Accepted Answer

True, so k=\frac{1}{2}

Question 11

What is the asymptote of f(x)?

Accepted Answer

y = 0

Question 12

True or false: All logarithmic functions pass through (b, 1).

Accepted Answer

True

Question 13

To solve \log_48x^2=2, you can rewrite the logarithm as an exponential equation...

Accepted Answer

True, so 4^2=8x^2

Question 14

When given points (5,121.5) and (6,364.5) in y=a\cdot b^xknowing b=3, how do we find a?

Accepted Answer

Use 121.5 / 35 = 1/2, Use 364.5 / 36 = 1/2

Question 15

What is the domain of g\left(x\right)=\log_4\left(x+5\right)-3?

Accepted Answer

x > -5

Question 16

If C\left(h\right)=120\left(0.5\right)^{\frac{h}{4}} how many hours will it take for only 15 mg of caffeine to remain?

Accepted Answer

12 hours

Question 17

If a premium's monthly cost can be modelled as y=2.1\left(1.0755\right)^x, how old is a person paying $145?

Accepted Answer

\log_{1.0755}\left(\frac{145}{2.1}\right)=58.2 years

Question 18

How can you rewrite log k = 3 using an exponential equation?

Accepted Answer

103 = k = 1,000

Question 19

If you answer a toss-up question in quiz bowl early enough you are penalized...

Accepted Answer

The other team getting to hear the rest of the question, then answer, Losing 5 points, but only if you interrupted the moderator

Question 20

If you answer a toss-up question in quiz bowl early enough because you understood harder clues, you earn...

Accepted Answer

A power, worth 15 points instead of 10, 3 bonus questions for your team alone to answer

Questions 20