The bookstore marked some notepads down from $3.00 but still kept the price over $2.00. it sold all of them. the total amount of money from the sale of the pads was $36.55. how many notepads were sold? what was the price of each notepad?

The number of notepads sold will be 17 and the price of each notepad is $2.15

Let's assume, the price of each notepad is X and the number of notepads sold is Y

As the price of each notepad is below $3.00 and over $2.00 , that means

X < 3.00 and X > 2.00

As the number of notepads sold is Y, so the total price of all X number of notepads will be : XY

Here it is given that, the total amount of money from the sale of the pads was $36.55

So, XY = 36.55

⇒ Y =

For X < 3.00 ,

Y > (when X is max, then Y will be min)

⇒ Y > 12.183

and for X > 2.00,

Y < (when X is min, then Y will be max)

⇒ Y < 18.275

As here Y is the number of notepads sold, so the value of Y must be a whole number. The minimum value of Y will be 13 and maximum value will be 18.

Now we will use hit and trial method

If Y= 13 , then X =

If Y= 14 , then X =

If Y= 15 , then X =

If Y= 16 , then X =

If Y= 17 , then X =

and if Y = 18 , then X =

So, for getting XY= 36.55 exactly, the value of X= 2.15 and the value of Y=17.

So, the number of notepads sold will be 17 and the price of each notepad is $2.15

coin flip

non-answer:

choosing

sorry if this isnt what you're looking for i dont really understand the question

part a

answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.

work shown:

n is the number of days after the experiment starts. the smallest n can be is n = 0 which means that 0 days have gone by, and we're at the start. to find out how large n should be, then replace f(n) with 16.13 and solve for n. use logarithms to isolate the exponent.

f(n) = 12*(1.03)^n

16.13 = 12*(1.03)^n

16.13/12 = (1.03)^n

1.34416666666667 = (1.03)^n

(1.03)^n = 1.34416666666667

log[ (1.03)^n ] = log[ 1.34416666666667 ]

n*log[ 1.03 ] = log[ 1.34416666666667 ]

n = log[ 1.34416666666667 ]/log[ 1.03 ]

n = 10.0062999823929

this rounds to n = 10 which is fairly close but not 100% perfect. so this is the largest n can be.

note: if you plug n = 10 into f(n), you'll get roughly 16.127 which rounds to 16.13 (this comes up again in part c)

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part b

answer: the y intercept is 12. it represents the starting height of the plant in cm.

work shown:

plug n = 0 into the f(n) function. simplify

f(n) = 12*(1.03)^n

f(0) = 12*(1.03)^0

f(0) = 12*(1)

f(0) = 12

on day n = 0, aka the starting point, the height f(n) is 12 cm

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part c

answer: the average rate of change is approximately 0.43061036458991 (round however you need to). this represents the average growth rate from day n = 3 to day n = 10. so the plant grew roughly 0.43 cm per day during this timespan, assuming you round to 2 decimal places.

work shown:

compute f(3)

f(n) = 12*(1.03)^n

f(3) = 12*(1.03)^3

f(3) = 13.112724 < we'll use this later

compute f(10)

f(n) = 12*(1.03)^n

f(10) = 12*(1.03)^10

f(10) = 16.1269965521294 < we'll use this later

now use the formula below with a = 3 and b = 10

aroc = average rate of change

aroc = [ f(b) - f(a) ]/[ b - a ]

aroc = [ f(10) - f(3) ]/[ 10 - 3 ]

aroc = (16.1269965521294 - 13.112724)/(10 - 3)

aroc = 3.0142725521294/7

aroc = 0.43061036458991

round this however you need to

note: the plant grew approximately 3.01 cm over 7 days, so roughly 0.43 cm per day is the average growth rate (if you were to round to 2 decimal places).