Question

Nadia swims at a rate of 50 meters per minute. Create a function f, where f(n) gives the number of meters Nadia swims given the number of minutes she swims, n.

Select the options to the empty boxes to correctly complete the equation for the function.

f(n) = 50 ____ ____

f n + - ● ÷

Some time ago, Carmen put an initial deposit of $150 into an account. After his initial deposit, he added more money to his account every two weeks. The table shows the amount of money in Carmen's account starting with his initial deposit.

Part A. How did the amount of money, f(w), in Carmen's account change every two weeks?

Select from the drop-down menus to correctly complete the sentence about the money in Carmen's account.

After Carmen's initial deposit, the amount of money his account

_______________ increased or decreased at a _____________ varying or constant rate.

Part B. Create the function f, where f(w) models the amount of money in Carmen's account given the number of weeks, w, after his initial deposit.

f(w) = _______ ● w ________ _________

40 80 150 450 + - ● ÷

Answer 1

if minutes she swims = n

how would you express "50 times minutes she swims" in ~~~math~~~ NOT words?

Answer 2

1(4 +46 ) = 50 To walk 50 meters in per minute she has to walk 80 feet a minute.

Answer 3

please do not put unrelated information from other problems

Answer 4

i didn't i just worked this out

Answer 5

the problem has nothing to do with walking

Answer 6

i meant to say swim but i put walk by accident

Answer 7

one more time

if n = minutes

then how can we express "50 times minutes" in math not words?

Answer 8

hint: "times" means multiplication

Answer 9

50 x 50

Answer 10

try one more time

Answer 11

n = minutes

50 * minutes = ?

Answer 12

7

Answer 13

???

Answer 14

n = minutes means we can replace "minutes" with "n" when we see minutes

so 50 * minutes = ?

Answer 15

n

Answer 16

50 x minutes = n

Answer 17

nope, one more time

Answer 18

write down "50 x minutes"

erase "minutes"

write "n" where minutes used to be

Answer 19

let me know what you get.

Answer 20

50 x minutes

erases minutes and put n where minutes used to

50 x n

Answer 21

good so 50 x n is your answer for A

Answer 22

oh i see it

Answer 23

for the next problem I need to see the table to answer it.

Answer 24

but wait there's no x

Answer 25

● is the same as x

Answer 26

oh ok

Answer 27

both of these symbols represent multiplication

Answer 28

ok

Answer 29

again, please post a screenshot of the table so I can work on the problem.

Answer 30

ok hold on

Answer 31

that's the table

Answer 32

ok

let's start by calculating the rate of change in f(w)

Answer 33

we use a formula called the rate of change formula

rate of change = [ f(x2) - f(x1) ] / (x2-x1)

Answer 34

now, let's look at the table where w = 0 and w = 2

what are the values of f(0) and f(2)? look at the table please.

Answer 35

on the time, w, in weeks

Answer 36

when w = 0, what is the value of f(0)? use the table to answer. your answer should be a number, not words.

Answer 37

f (0) = 0

Answer 38

look at the table, one row at a time.

the left column tells you w
the right column tells you f(w) for that same w

for example, if you look at the last column, w = 8 and f(w) = f(8) = 470

now, use this same logic to tell me what f(0) is

Answer 39

w = 0 and f(w) = 150 = f(0) = 150

Answer 40

good

Answer 41

what about f(2)?

Answer 42

w = 2 and f(w) = 230 = f(2) = 230

Answer 43

good

so if f(2) = 230 and f(0) = 150

calculate: [ f(2) - f(0) ] / (2 - 0)

be careful with parentheses/order of operations

Answer 44

f(4)

Answer 45

am i correct ?

Answer 46

your answer should be a number not including f

Answer 47

f(2) = 230 and f(0) = 150

Answer 48

replace "f(2)" with 230 and "f(0)" with 150

so calculate [ f(2) - f(0) ] / (2 - 0) = ?

Answer 49

230 - 150 ? solve ? like that

Answer 50

yes, but for the entire expression

Answer 51

[ f(2) - f(0) ] / (2 - 0) = (230-150)/2 = ?

Answer 52

40

Answer 53

good so the weekly rate of change is 40 (to speed things up, I will tell you that the table has a constant rate of change of 80, you can verify this on your own time using the same formula)

Answer 54

now, we know our "intercept" or intial value is f(0) = 150

so we can now write an equation like so:

Answer 55

f(w) = (weekly rate of change) * w + initial value

replace "weekly rate of change" with 40 and "initial value" with 150

re-write the equation now.

Answer 56

BRB

Answer 57

ok

Answer 58

f(w) = 40 x w + 150

Answer 59

Good that's your answer for the problem

Answer 60

Wait is Carmen's account increased or decreased ?

Answer 61

and varying or constant rate ?

Answer 62

Is the money going up or down?

Answer 63

down

Answer 64

Look at the table.

Answer 65

i meant up i meant sorry

Answer 66

good so the money is increasing

Answer 67

and what about the rate ?

Answer 68

I already said it was constant

Answer 69

oh wait ok

Answer 70

could you help me with another one ?

Answer 71

have to get going, sorry

Answer 72

please right quick

Answer 73

Part A

There is a function f, where f(n) = 1200n + 3500 represents the number of people in a town who owned a smartphone n years after 2007. How many people owned a smartphone in this town in the year 2010 ?

Enter your answer in the box

____________

Part B

There is a function p, where p(x) represents the percent of adults in the United States who owned a smartphone x years after 2011. What does p(5) = 68 represent?

Select from the drop-down menus to correctly complete the sentence.

In the year ___________ 2011 or 2016 ____________ 5 or 68 or 5% or 68% of the adults in the United States owned a smartphone.