1. identify the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in.

a: l = 180 in2 ; s = 205 in2
b: l = 225 in2 ; s = 250 in2
c: l = 90 in2 ; s = 115 in2
d: l = 120 in2 ; s = 162 in2

2. identify the lateral area and surface area of a regular triangular pyramid with base edge length 14 cm and slant height 15 cm.

a: l = 630 cm2 ; s = 484.7 cm2
b: l = 315 cm2 ; s = 399.9 cm2
c: l = 630 cm2 ; s = 399.9 cm2
d: l = 315 cm2 ; s = 484.7 cm2

3. identify the lateral area and surface area of a regular hexagonal pyramid with base edge length 60 m and slant height 35 m.
a: l = 6,300 m2 ; s = 15,653.1 m2
b: l = 6,300 m2 ; s = 11,700 m2
c: l = 5,250 m2 ; s = 14,603.1 m2
d: l = 12,600 m2 ; s = 21,953.1 m2

4. identify the lateral area and surface area of a right cone with radius 6 cm and slant height 13 cm.

a: l = 78 cm2 ; s = 114 cm2
b: l = 245 cm2 ; s = 608.9 cm2
c: l = 245 cm2 ; s = 358.1 cm2
d: l = 78 cm2 ; s = 358.1 cm2

5. identify the lateral area and surface area of a right cone with diameter 8 m and slant height 13 m, rounded to the nearest tenth.
a: l = 163.4 m2; s = 527.8 m2
b: l = 163.4 m2; s = 213.6 m2
c: l = 326.7 m2; s = 527.8 m2
d: l = 326.7 m2; s = 213.6 m2

l.jnl.j/n.m,lm,

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)

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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).