SOLUTION: A bacteria colony begins with 6 individuals and doubles in size every hour. Write down a recurence for a in n terms, the population at the beginning of hour n, and solve it. How ma

Algebra ->  Proofs -> SOLUTION: A bacteria colony begins with 6 individuals and doubles in size every hour. Write down a recurence for a in n terms, the population at the beginning of hour n, and solve it. How ma      Log On


   

Question 850169: A bacteria colony begins with 6 individuals and doubles in size every hour. Write down a recurence for a in n terms, the population at the beginning of hour n, and solve it. How many hours elapse until the population exceeds one million?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
EDITED: No need for any Change of Base.

n hours_____________Count
0___________________6
1___________________6*2
2___________________6%2A2%2A2=6%2A2%5E2
3___________________6%2A2%2A2%2A2=6%2A2%5E3
.
.
.
n___________________6%2A2%5En

Relation: highlight%28a=6%2A2%5En%29, n is the count of finished hours; a is the count of bacteria.

If a=1000000, what is n?
6%2A2%5En=1000000
2%5En=1000000%2F6=166666%262%2F3
2%5En=166666%262%2F3
-
log%2810%2C2%5En%29=log%2810%2C+166666%262%2F3%29
n%2Alog%2810%2C2%29=log%2810%2C+166666%262%2F3%29
n=log%2810%2C166666%262%2F3%29%2Flog%2810%2C2%29
n=5.2218%2F%280.30103%29
highlight%28n=17.34%29 hours
17 hours 21 minutes