Question

during the fall, squirrels gather nuts and store them to prepare for winter. as winter approaches, nuts become more scarce and squirrels start eating the nuts they have in their stores. this function models the number of nuts a squirrel has in its store t weeks after october 1:
$y = -70(t - 10)^2 + 7,000$
what is the greatest number of nuts the squirrel ever has in its store?
_____ nuts

Explanation:

Step1: Analyze the function form

The given function is \( y = -70(t - 10)^2 + 7000 \), which is in the vertex form of a quadratic function \( y = a(x - h)^2 + k \), where \( a=-70 \), \( h = 10 \), and \( k = 7000 \).

Step2: Determine the maximum value

For a quadratic function in vertex form, if \( a<0 \), the parabola opens downward, and the vertex \( (h,k) \) is the maximum point. Here, \( a=-70<0 \), so the maximum value of \( y \) occurs at \( t = 10 \), and the maximum value of \( y \) is \( k \), which is \( 7000 \).

Answer:

7000