Math Snap

STEP 1

Assumptions1. The world's population growth rate is1.9% per year since1945. The world's population was approximately4 billion in19753. We are looking for a function that represents the world's population, in billions of people, t years since19754. The growth is exponential, not linear

STEP 2

The general form of an exponential function is$$(t) =0 \times (1 + r)^t$$where- $(t)$ is the population at time $t$,
- $0$ is the initial population,
- $r$ is the growth rate, and- $t$ is the time since the initial population was measured.

STEP 3

Given that the world's population was approximately billion in1975, we can set $0 =$.

STEP 4

The growth rate is given as1.9% per year. In the exponential function, this rate needs to be expressed as a decimal. So, we convert1.9% to0.019.

STEP 5

Substituting the values of $0$ and $r$ into the exponential function, we get$$(t) =4 \times (1 +0.019)^t$$

implify the expression inside the parentheses$$(t) =4 \times (1.019)^t$$This function represents the world's population, in billions of people, t years since1975. Therefore, the correct answer is A) $(t)=4(1.019)^{t}$.