The suspended copper levels y (in parts per billion) in Silver Bow Creek are bel

Question

The suspended copper levels y (in parts per billion) in Silver Bow Creek are believed to increase quadratically with the flow rate x of Silver Bow Creek (in cubic feet per

second), according to the following model:

y = 4 + 0.2x + 0.015x2 + e.

a) What is the mean level of suspended copper in Silver Bow Creek when the creek is flowing at a rate of 600 cubic feet per second?

b) How much would the mean value of y increase when the value of x increases from 600 cubic feet per second to 700 cubic feet per second?

Explanation / Answer

The suspended copper levels y (in parts per billion) in Silver Bow Creek are believed to increase quadratically with the flow rate x of Silver Bow Creek (in cubic feet per

second), according to the following model:

y = 4 + 0.2x + 0.015x2 + e.

(a) What is the mean level of suspended copper in Silver Bow Creek when the creek is flowing at a rate of 600 cubic feet per second?

so here x = 600 cubic feet per second

so suspended copper levels at given x =

y = 4 + 0.2 * 600 + 0.015 * 6002 = 5524 parts per billion

(b) at x = 600 cubic feet per second copper level => y = 5524 parts per billion

at x = 700 cubic feet per second copper level => y = 4 + 0.2 * 700 + 0.015 * 7002 = 7494 parts per billion

so increase in mean value of suspended copper = (7494 - 5524)parts per billion = 1970 parts per billion

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