Answer
$2025$
Work Step by Step
Substituting the expression of $c$ with $"<200",$ the given equation, $
c=-9.4t+431
,$ becomes
\begin{array}{l}\require{cancel}
-9.4t+431\lt200
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-9.4t\lt200-431
\\
-9.4t\lt-231
.\end{array}
Dividing both sides by a negative number (and consequently reversing the sign), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
t\gt\dfrac{-231}{-9.4}
\\
t\gt24.574468085106382978723404255319
.\end{array}
Hence, the cigarette consumption will be less than $200$ billion in $t=25$ years after $2000$ or in the year $
2025
.$
