Question

suppose for children under 5, the world mortality rate m per 1000 live births can be modeled by the equation m = - 1.61n + 74.46, where n is the number of years since 2000.
a. according to the accompanying graph, is the mortality rate increasing or decreasing?
b. use the equation to find the year in which the mortality rate will be 42.

a. choose the correct answer below
decreasing
increasing

b. the year in which the mortality rate will be 42 is □.

Explanation:

Step1: Analyze the slope of the linear - equation

The mortality - rate equation is $M=-1.61n + 74.48$, where the slope $m=-1.61<0$. A negative slope indicates a decreasing function. Also, from the graph, we can see the line is going downwards as $n$ (years) increases, so the mortality rate is decreasing.

Step2: Solve for $n$ when $M = 42$

Set $M = 42$ in the equation $M=-1.61n + 74.48$. We get the equation $42=-1.61n + 74.48$.
First, subtract 74.48 from both sides: $42−74.48=-1.61n$, which simplifies to $-32.48=-1.61n$.
Then, divide both sides by $-1.61$: $n=\frac{-32.48}{-1.61}=20$.

Answer:

a. Decreasing
b. 20