Question

The population of the world grows exponentially at a rate of 1.1% per year.

Answer 1

Answer:

4

Step-by-step explanation:

Every year, the world grows by 1.1%. Converting to a decimal, we can divide by 100 to get 1.1% = 0.011. This means that the world grows by 0.011 exponentially each year. To put this into an expression, we can add 1 to our percentage to get 1.011. This represents 1 = 100% (the original population) and the growth of 1.1% = 0.011. We multiply the rate including the growth by the population to get the population after one year. After the first year, we have

population * 1.011 as the new population after one year. We do that for every year, so the second year's population is population*(1.011)*(1.011) and so on. If x represents the amount of years, then the population can be represented as

(original population)*1.011ˣ

Therefore, to get from 7 billion to 7.31 billion, we have

7 billion * 1.011ˣ = 7.31 billion

divide both sides by 7 billion to relatively isolate the x

1.011ˣ = 7.31/7

Another way of writing this is

log (base 1.011) (7.31/7) = x

≈ 3.96

Rounding to the nearest whole number, we get 4 as our answer