a. To convert the given function to pounds, we need to multiply the result by 2204.62 (since 1 metric ton = 2204.623 pounds).
The given function in pounds:
y = 1.36(2204.62)x^2 + 27.8(2204.62)x + 304(2204.62)
Now we want to find the year when 500 million pounds were imported:
500,000,000 = 2998.323x^2 + 61328.156x + 670000.48
Now, we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
where, a = 2998.323, b = 61328.156, and c = 670000.48 - 500,000,000
x = (-61328.156 ± √(61328.156^2 - 4(2998.323)(-499329999.52)))/(2*2998.323)
x ≈ 4.624 and x ≈ -45.909
Since the year cannot be negative, we take x = 4.624, which means that approximately in the year 1994 (1990 + 4.624), 500 million pounds of biscuits, pasta, and noodles were imported.
b. Now we will find the year when 575 million pounds were imported.
575,000,000 = 2998.323x^2 + 61328.156x + 670000.48
Now, we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac))/(2a)
where, a = 2998.323, b = 61328.156, and c = 670000.48 - 575,000,000
x = (-61328.156 ± √(61328.156^2 - 4(2998.323)(-574329999.52)))/(2*2998.323)
x ≈ 6.514 and x ≈ -50.122
Since the year cannot be negative, we take x = 6.514, which means that approximately in the year 1996 (1990+6.514), 575 million pounds of biscuits, pasta, and noodles were imported.
or the period 1990-2003, the amount of biscuits, pastas, and noodles y (in thousands of metric tons)imported into the united states ca be modeled by the function y=1.36(xsquared)+ 27.8x+304 where x is the number of year since 1990.
a.write and solve an equation that you can use to approximate the year in which 500 million pounds of biscuits, pasta, and noodles were imported.
b. write and solve an equation that you can use to approximate the year in which 575 million pounds of biscuits, pasta and noodles were imported.
1 answer
1 answer