HELP ASAP (MATH)

Pyramid tents were popular for a time during the 19th century. Although their popularity declined during the
20th century, they have recently begun to regain popularity. The design is ideal for shaping canvas, and it only
requires one pole and some stakes to secure it. Joe wants to make a right square pyramid tent and is considering
two different sizes. He will either make one with a base that is 10 feet by 10 feet and has a height of 12 feet (Tent
1), or he will make one with a base that is 12 feet by 12 feet and has a height of 8 feet (Tent 2).
Part A
Calculate the volume of each proposed pyramid tent
Tent 1. Base: 10 x 10 ft Height: 12 ft Tent 2 - Base: 12 x 12 ft Height: 8 ft
Part B
Which tent would you recommend Joe make if he wants more interior space?

PART - A : tent - 1 volume = 400 cubic ft

Tent -2 volume = 384 cubic ft.

PART - B : I recommend Joe to make the tent -1 with base 10x10 ft. as it has more volume

Step-by-step explanation:

PART - A:

tent 1 :

 Base = 10 x 10ft

 Height= 12 ft

 Volume = (1/3) (10x 10) (12)

 = (1/3) (100) (12)

= 400 cubic ft.

Tent 2:

 Base = 12 x 12 ft

 Height= 8 ft.

 Volume = (1/3) (12 x 12) (8)

= 384 cubic ft.

PART - B:

I recommend Joe to make the tent -1 with base 10x10 ft. as it has more volume

the answer is c hope it

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).