for the period 1990-2003, the amount of biscuits and pasta y(in thousands of tons) imported to the united states can be modeled by the function: y=1.36x^2+27.8x+77

how many tons obiscuits and pasta were imported to the states in 1999?
in which year was the maximum imported?
what was the maximum amount imported?

You did not define x

I assume x represents the number of years since 1990

So for 1999 , x = 9
sub in 9 and evaluate

YOur equation represents a parabola,
find the vertex ...

since the parabola opens up, there will be a minimum and a quick mental calculation will show that to be a negative x
----> must have happened before 1990

Since all the terms are positive, the value of y will increase as x increases, so the max will be in 2003
or when x = 13
just evaluate for x = 13

To find the amount of biscuits and pasta imported to the United States in 1999, we can substitute the value of x = 1999 into the given function y = 1.36x^2 + 27.8x + 77.

Let's calculate it:

y = 1.36(1999)^2 + 27.8(1999) + 77

Simplifying further:

y = 1.36 * 3,996,001 + 55,602.2 + 77

y ≈ 5,436,802 + 55,602.2 + 77

y ≈ 5,492,481.2

So, approximately 5,492,481.2 tons of biscuits and pasta were imported to the United States in 1999.

To determine the year with the maximum amount imported, we need to find the vertex of the given quadratic function. The vertex is obtained by calculating the x-coordinate using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1.36 and b = 27.8.

x = -27.8 / (2 * 1.36)
x = -20.441

Since the function is a quadratic, the maximum occurs at the vertex. In this case, the maximum value represents the highest amount imported. Therefore, the maximum imported occurred in the year - approximately 20.441. Since the year should be a whole number, we round it to the nearest year, which is 20.

Therefore, the maximum imported occurred in the year 20.

To find the maximum amount imported, we substitute the x-coordinate of the vertex (-20) into the given equation y = 1.36x^2 + 27.8x + 77.

Let's calculate it:

y = 1.36(-20)^2 + 27.8(-20) + 77

Simplifying further:

y = 1.36 * 400 + (-556) + 77

y = 544 + (-556) + 77

y ≈ 65

Therefore, the maximum amount of biscuits and pasta imported to the United States was approximately 65 thousand tons.