Question

An astronaut was exploring the moon of a distant planet, and found some glowing goo at the bottom of a very deep crater. She brought a 10-gram of the goo to her laboratory. She found that when the goo was exposed to light, the total amount of goo increased by 100% every hour. How much goo will she have sfter 1 hour?After 2 hours? After 3 hours? After n hours?

Answer 1

20 ; 40 ; 80 ; 10(2^n)

Explanation:

Given that:

Initial amount of goo (p) = 10 gram

Total amount of goo increased by 100% every hour ;

How much goo will she have sfter 1 hour?After 2 hours? After 3 hours? After n hours?

Using the relation :

Final amount = initial * (1 + rate)^t

Rate = 100% = 100/100 = 1

t = number of hours

Hence, after 1 hour :

Final amount = 10(1 + 1)^1

Final amount = 10(2)^1 = 20 grams

After 2 hours : t = 2

Final amount = 10(1 + 1)^2

Final amount = 10(2)^2 = 10 * 4 = 40 grams

After 3 hours ; t = 3

Final amount = 10(1 + 1)^3

Final amount = 10(2)^3 = 10 * 8 = 80 grams

After n hours ; t = n

Final amount = 10(1 + 1)^n

Final amount = 10(2)^n grams