Question

If the world's population increased exponentially from 5.937 billion in 1998 to 7.238 billion in 2014 and continued to increase at the same percentage rate between 2014 and 2015, calculate what the world's population would have been in 2015.

Answer 1

Answer: The world's population in 2015 would have been 7.333 billion.

Step-by-step explanation:

• Since the increase in population is an exponential one. It then follows a geometric progression defined by, $T_{n}$ = $ar^{n - 1}$

• Where $T_{n}$ is the nth term, a is the 1st term, r is the common ratio.

•  Therefore, the population in 1998 is the first term a = 5.937 billion. The population in 2014 corresponds to the 17th term (i.e., n = 17) = 7.238 billion.

Hence, $T_{n}$ = $ar^{n - 1}$

7.238 billion = 5.937 billion × $r^{17 - 1}$

$r^{16}$ = (7.238 billion) ÷ (5.937 billion)

= 1.219

r = $\sqrt[16]{1.219}$

r = 1.0125

To get the population in 2015, which is the 18th term. We use

$T_{n}$ = $ar^{n - 1}$

$T_{18}$ = 5.937 billion × $1.0125^{18 - 1}$

= 5.937 billion × $1.0125^{17}$  

= 5.937 billion × 1.235

$T_{18}$ = 7.333 billion

Answer 2

Answer:

The world's population at 2015 is 7.328 billion

Step-by-step explanation:

An exponential increase in population can be represented by the equation below:

F = p(1+r)ᵗ .....1

Where;

F = final population after time t

p = initial population

r = rate of increase in population per time

t = time

Given;

F = 7.238 billion

p = 5.937 billion

t = 2014 - 1998 = 16 years

To determine the value of r from equation 1, making r the subject of formula.

1+r = (F/p)^(1/t)

r = (F/p)^(1/t) - 1

Substituting the given values.

r = (7.238/5.937)^(1/16) - 1

r = 1.01246 - 1

r = 0.01246

Therefore, the population in 2015 can be calculated using the equation 1.

t = 2015 - 1998 = 17

p = 5.937 billion

r = 0.01246

Substituting the values into equation 1.

F(2015) = 5.937(1+0.01246)^17

F(2015) = 7.328 billion.

So, the population at 2015 is 7.328 billion.