Next, you'll test your hypothesis from part A by examining the reaction times of vinegar and baking soda in water at four different temperatures. You'll carry out the reaction using water at room temperature
(about 25°C), 40°C, 60°C, and 80°C. Make sure that you use the same amounts of vinegar and baking
soda for all three three trials.
Gather all the materials, and perform these steps for each trial:
1. Heat at least 1 cup (60 milliliters) of water to the required temperature (refer to the data table).
Water may be heated on a stove, on a hot plate, or in a microwave oven.
2. Measure and record the actual temperature of the water.
3. Measure 1 tablespoon (15 milliliters) of the water into the cup.
4. Add teaspoon (1.5 grams) baking soda to the water, and stir until it is dissolved. The solution will
be clear.
5. Measure 1 tablespoon (15 milliliters) of vinegar, but do not pour it into the cup yet.
6. Very quickly, do all of the following:
a. Pour the measured vinegar into the cup.
b. Start the stopwatch.
C. Stir or carefully swirl the substances in the cup.
7. The chemical reaction will produce bubbles. You'll be able to see the bubbles and hear them pop.
Watch and listen for when the reaction stops. When it looks and sounds like it has finished, stop the
stopwatch.
8. Record the reaction time in the data table.
9. Discard the solution down the drain, and rinse the cup.
10. Repeat steps 1-9 of this procedure, doing three trials for each water temperature. Record the
average temperature and reaction time for each set of the three trials. Read this math review to
know how to calculate average of a data set.

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)

=====================================

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

=====================================

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).

m

step-by-step explanation:

they charge the same amount at 20 minutes.

step-by-step explanation:

its d hope this