The first questions are about estimates. Please see your class notes for details and remember:

$($i$)$ an estimate is not a guess, and $($ii$)$ the best approach is to break down the problem into small

pieces you can either observe or reasonably estimate, then combine to get the answer. You should

not need to look up any numbers.

$(1)$ The population of the United States is about $330$ million people.

$($a$)$ Estimate how many disposable water bottles are used by that population in one year.

$($b$)$ If you were to stack those bottles end$-$to$-$end, about how long $($in miles or kilometers$)$

would that stack of bottles be$?$

As always, state your reasoning clearly.

$(2)$ The local newspaper reports that a town$$s water utility provides $6$ million gallons of water

per day. Estimate how many people live in the town. Don$$t look up any numbers, just

estimate based on reasoning and what you already know or can observe. Remember: an

estimate isn$$t just a simple guess. Try breaking down the question into smaller elements:

starting with your own experience, estimate how much water the average person uses in a

day for all purposes, and use that to estimate the answer. Show all your reasoning clearly.

$(3)$ Estimate the number of hairs on your head. Don$$t look up any numbers, just estimate

based on reasoning and what you already know or can observe.

$(4)($a$)$ Estimate the annual $($cow$)$ milk production in the United States. Express your answer

as a weight in pounds. $($b$)$ Estimate the monetary value $($in dollars$)$ of all that milk. As in

the first problem, don$$t look up any numbers. As always, show all your reasoning clearly.

$(5)$ In empty space $($aka vacuum$),$ light travels at speed c $=3\backslash$times $108$ m$/$s$.($The speed of light

is a fundamental physical constant, so we give it its own symbol, c$.)$

$($a$)$ Convert this speed to miles per second, showing each of your steps.

$($b$)$ How far, in feet, does light travel in $1$ nanosecond $($that$$s $109$

s or one billionth of a

second$)?$

$($c$)$ A lightyear is the distance light travels in one year. How many meters are there in $1$

lightyear?

$(6)$ Two more questions using the speed of light:

$($a$)$ The newspaper reported that the radio signal $($which also travels at speed, c$)$ from

the New Horizons spacecraft took about $6$ hours to reach the earth. How far away, in

kilometers, was the spacecraft?

$($b$)$ The earth is about $150$ million km from the sun. How long $($in minutes$)$ does it take

light emitted from the sun to reach the earth?