Did I answer this correctly? Need help figuring this out..

[wunnymush13]

Did I answer this correctly?

I feel like I got this wrong but I'm not entirely sure.. if someone could help me out please. I'm fairly certain it's incorrect due to well.. it just doesn't make sense, lol.


Here is the question:
The current world population is 7 billion people and growing at a rate of 1.11% per year according to the United Nations.
a) In what year will the world population reach 10 billion people?
b) Suppose that the world population growth rate remains at 1.11% per year for the next 10 years, then suddenly increases to 1.20% per year for the following 10 years. What will the world population be 20 years from now?

Here is my answer:

a)
Equation is 7=1.11x
7 being the current world population of 7 billion
1.11 being the growth percentage
x being the years

10=1.11x
9.9000=x. (Approximately 9 years)
The world population will reach 10 billion people in 2020.

b)
7=1.11x
7=1.11(10)
7=11.1
Population in 10 years = 11.1 billion.

11.1=1.20(20)
11.1=20
Population in 20 years = 20 billion.

 

[tkhunny]

You should know that these are EXPONENTIAL functions. You don't seem to be using anything exponential.

\(\displaystyle 7\cdot 1.11^{x} = 10\)

Solve for x.

\(\displaystyle 7\cdot 1.11^{10}\cdot 1.20^{10} = ??\)

 

[srmichael]

...except the rate of growth is 1.11% or 0.0111 as a decimal, thus:

\(\displaystyle 7\cdot 1.0111^{x} = 10\)

Solve for x.

\(\displaystyle 7\cdot 1.0111^{10}\cdot 1.0120^{10} = ??\)

 

[wunnymush13]

Okay that sounds better. Now for the first equation, I solve for the exponent x, and that would be the population after 10 years?

 

[wunnymush13]

Woops, not done. Now for the 2nd equation, why does the exponent become 10? And wouldn't you add the 1.0120^10 because you're adding another ten years, not multiplying?