Look for a pattern in the first three equations. Then, fill in the missing numbers in the rest of the series of equations. 1= 1 · 2⁄2
1 + 2 = 2 · 3⁄2
1 + 2 + 3 = 3 · 4⁄2
1 + 2 + 3 + ? = ? · ?⁄?
1 + 2 + 3 + ? + ? = ? · ?⁄?

Solve the following equations.
a. 11w = 88
b. 7u = 210
c. v ÷ 81 = 9
d. c ÷ 4 = 16
For the following problems, tell what operation(s) you need to use. Then, write and solve an equation for each problem.

Bill bought a computer and a printer for a total of $650. The computer cost $525. How much did he pay for the printer alone? (Let p stand for the cost of the printer.)
Bonnie loves to order products online. She ordered 27 products from one company, but unfortunately, some items were back-ordered, so she received only 19 items. How many items were missing from her order? (Let m stand for the number of missing items.)
Terri bought four lipsticks for a total cost of $20. Assuming each lipstick cost the same amount, how much did one lipstick cost? (Let l stand for the cost of one lipstick.)
Brian is conducting surveys for a research paper. Each survey takes him about 10 minutes to complete, so he can get 6 done per hour. At this rate, how many hours will it take Brian to complete 30 surveys? (Let h stand for the number of hours.)
Andy played golf three times during his vacation. His scores were 92, 87, and 88. What was his average golf score during his vacation? (Let A stand for the average.)
Tickets to a local basketball team’s games cost $12 each. Brendon and Ed each bought tickets to four games. How much did they spend on tickets altogether? (Let t stand for the amount spent on tickets.)

f

step-by-step explanation:

f

16.9 times 2.85

step-by-step explanation:

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).