Question

You have a 90-pound calf you are raising for a \(4-\mathrm{H}\) project. You expect the calf to gain 65 pounds per month. In how many months will the animal weigh 1000 pounds?

Short answer

It will take approximately 14 months for the calf to reach a weight of 1000 pounds.

Step-by-step solution

Identify the Known Variables

The weight of the calf initially is 90 pounds. The calf gains weight at a rate of 65 pounds per month. The target weight to be achieved is 1000 pounds. Thus, the known are: Initial weight = 90 pounds, Gain rate = 65 pounds per month, Target weight = 1000 pounds.

Derive the Linear Function

To find out in how many months the calf will reach a weight of 1000 pounds, derive a formula from the given information. The formula relates the final weight (Fw) of the calf, the initial weight (Iw) of the calf, the rate of weight gain (R) and the time in months (t). The formula can be denoted as: Fw = Iw + R * t.

Substitute the Known Variables into the Equation and Solve for Unknown

Substitute the initial weight (90 pounds), the rate of weight gain (65 pounds per month), and the target final weight (1000 pounds) into the equation Fw = Iw + R * t. Then solve for 't'. The equation now looks like this: 1000 = 90 + 65 * t. Solving the equation, subtract 90 from both sides to get: 910 = 65 * t. Dividing both sides by 65 gives: t = 910 / 65.

Calculate the Required Time

Calculate the value of \(t\) from the equation from previous step. The result is the time in months that it will take for the calf to reach a weight of 1000 pounds. So, \(t = 910 / 65 \approx 14\) months.