in Example 3, assume the world population increased by 1.5% each year. Write an equation to model this situation. Estimate the year when the world population was 7 billion.

an increase of 1.5% per year means that if the initial quantity is A.

After one year that quantity is A + A*0.015 = A*1.015

After another year we have other 1.5% increase, so now the quantity is:

A*1.015 + 0.015*A*1.015 = A * (1.015) ^2

then, after x years, the quantity is:

Q = A * (1.015) ^x

Now, this also works for negative values of x.

In 2019 the world population was 7.8 billion, we want to find x such the population was 7 billion. If x = 0 we are in year 2019, then A = 7.8 billion

we can solve this as:

(7 billion) = (7.8 billion) * (1.015) ^x

7/7.8 = (1.015) ^x

x = ln (7/7.8) / ln (1.015) = - 7.3

So the world population was around 7 billion around 7 years ago, in 2019 - 7.3 = 2011.7