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Question

# The function $f(x)=3462 \cdot 0.925^x$ represents the population of a town, where $x$ is the number of years since 1996.What is the $y$-intercept of the function, and what does it mean in the context of the problem?

Solution

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$\text{Given function in problem : }f(x)=3462\cdot(0.925)^x$

$y$-intercept of any function is the point on the $y$-axis from where the graph of function intersect thus at $y$-intercept value of $x=0$.

So the $y$-intercept of the function $f(x)=3462\cdot(0.925)^x$ can be found out by putting $x=0$.

$f(x)=3462\cdot(0.925)^0=3462\cdot1=3462$

$\textbf{y-intercept : }(0,3462)$

$\textbf{In context of problem it means the initial population of town which means population of town in 1996}$

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