Question

In January $1990$ the world's population was $5.3$ billion. Assuming a growth rate of $2$ percent per year, the world's population, in billions, for $t$ years after $1990$ can be modeled by the equation $P=5.3{\left(1.02\right)}^t$. With the help of the model, calculate the growth in population from January $1995$ to January $1996$.

• A. $106,000,000$
• B. $114,700,000$
• C. $117,000,000$
• D. $445,600,000$
• E. $562,700,000$

Answer 1

Answer: (C)

$117,000,000$

According to the model, the world's population in January $1995$ was $5.3(1.02{)}^5$ and in January $1996$ was $5.3(1.02{)}^6$.

Therefore, the population growth from Jan $1995$ to Jan $1996$, in billions was $5.3(1.02{)}^6-\mathrm{5..3}(1.02{)}^6=5.3\left(1.02{)}^5\right(0.02\left)\right({10}^9)\approx 117,000,000$