Question

The world population in the year 2011 was approximately 7 x 109 people. If the population doubles in 100 years, how many people will be on the earth in the year 2111? Write your answer in scientific notation.

Answer 1

1526

Answer 2

\[7\times 10^9\] right?

Answer 3

double that number to get \(14\times 10^9=1.4\times 10^{10}\)

Answer 4

in scientific notation 1.526*10^3

Answer 5

\[(7*109)^{2^{n}}\]

n=(2111-2011)/100

Answer 6

Look at the number line
I_________I_____________I__________________I........______________I
2011 2111 YEAR
To get from the year 2011 to 2111 you have (2111-2011)=100 Years
You stated that the population doubles in 100 years. What does that mean algebraically?
Well if you have x and it doubles you have 2x, so you multiply by 2.
So if you started with a population say
5.3X10^7 and it doubles you basically do the following:
2*(5.3X10^7)
2*5.3 X 10^7
10.6 X 10^7
But recall scientific notation we need that 10.6 to be less than 10.
We simply move the decimal to the left over one space
1.06 X 10^ ?
What goes in that question mark?
So 10.6 X 10^7= 106000000. you are moving the decimal 7 places over
If you want the same number but expressed correctly in scientific notation you have
1.06 X10^8 because this equals 1060000000 since it took one more space to the right to move over to get 106000000.