Question

On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated. Based on this information, predict the day on which the Moon's surface is 50% illuminated and 100% illuminated.
illuminated.
PLEASE HELPPPPPPP!!!!!!!!!!!​

Answer 1

Answer:

50%: day 13

100%: day 26

Step-by-step explanation:

We are given two days and the amount of the moon that is illuminated. The two days are points on a straight line.

(1, 0.02), (2, 0.06)

y = mx + b

m = (0.06 - 0.02)/(2 - 1) = 0.04

y = 0.04x + b

0.02 = 0.04(1) + b

b = -0.02

y = 0.04x - 0.02

We want y = 50% = 0.5

0.04x - 0.02 = 0.5

0.04x = 0.52

x = 13

y = 100% = 1

0.04x - 0.02 = 1

0.04x = 1.02

x = 25.5

Answer 2

Answer:

Day 13= 50%

Day 26=100%

Step-by-step explanation:

Answers vary. Sample response: A simple approach is to attempt a linear model starting at Day 1. If the illumination is increased by 4% every day, then after 11 more days (after Day 2) it reaches 50%. In 13 more days, illumination reaches 100%. This gives a prediction of Day 13 for 50% and Day 26 for 100%.