Question

HELP PLEASE! ANSWER ALL QUESTIONS

1. Tim and Kim took 4.6 hours to complete a 25.3 mile kayaking trip. If they wanted to paddle for 3 hours on their next trip, how far should they plan to go?

2. Kara had saved $10 and saves $25 from her paycheck every week. A. Write a linear function equation expressing the amount of money Kara has saved as a function of the number of weeks, t, since the year began. B. How long will it take for Kara to have $335 in savings?

3. While burning, a candle 12 inches tall decreases by 1.75 inches per hour. A. Which type of function (linear, quadratic, exponential) best describes this situation. explain your reasoning. B. Write a function equation, y, that expresses the height of the candle in inches as a function of the number of hours the candle has burned. C. How long will it take for the candle to have burned down to half its original length? Write the equation/inequality from the following graph

Answer 1

Problem 1

speed = distance/time

speed = (25.3 miles)/(4.6 hours)

speed = 5.5 mph

Then,

distance = speed*time

distance = (5.5 mph)*(3 hours)

distance = 16.5

Answer: 16.5 miles

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Problem 2

The linear function would be f(t) = 25t+10

The slope 25 tells us how much Kara saves from week to week. It's the rate of change. The 10 is her starting amount. It's the y intercept.

Replace f(t) with 335 and solve for t.

f(t) = 25t+10

335 = 25t+10

335-10 = 25t

325 = 25t

25t = 325

t = 325/25

t = 13

It will take 13 weeks for Kara to have $335 in her savings.

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Problem 3

This is a linear function because the height decreases the same amount for each hour. The slope is -1.75 to represent the decrease of 1.75 inches per hour. The y intercept is 12 because it's the starting height.

The function would be f(t) = -1.75t + 12

Replace f(t) with 6 to determine when it reaches half its starting height.

f(t) = -1.75t + 12

6 = -1.75t + 12

6-12 = -1.75t

-6 = -1.75t

-1.75t = -6

t = -6/(-1.75)

t = 3.42857 approximately

Round that value however needed.