Question

In a laboratory experiment, a scientist is investigating the rate of homeglobin production in a culture of red blood cells. The rate of production, p(t), in milligrams per hour (mg/hr), can be modeled by the polynomial function where t represents the time in hours: p(t) = -0.5t⁴ + 4t³ - 10t² + 8t + 5. What is the rate of homeglobin production at t = 2 hours?

1) -2 mg/hr
2) 10 mg/hr
3) 18 mg/hr
4) 25 mg/hr

Answer 1

The rate of hemoglobin production at t = 2 hours is found by substituting t = 2 into the polynomial function, yielding a result of 5 mg/hr, which corresponds to option 4).

Step-by-step explanation:

The student has asked to find the rate of hemoglobin production at t = 2 hours using a given polynomial function p(t) = -0.5t⁴ + 4t³ - 10t² + 8t + 5. To find the rate, we need to substitute t with 2 hours into the polynomial function.

Substitute t = 2 into the polynomial function:
p(2) = -0.5(2)⁴ + 4(2)³ - 10(2)² + 8(2) + 5
p(2) = -0.5(16) + 4(8) - 10(4) + 16 + 5
p(2) = -8 + 32 - 40 + 16 + 5
p(2) = 5

Therefore, the rate of hemoglobin production at t = 2 hours is 5 mg/hr, which is option 4).

To find the rate of homeglobin production at t = 2 hours, we need to evaluate the function p(t) at t = 2. Substitute t = 2 into the function:

p(2) = -0.5(2)^4 + 4(2)^3 - 10(2)^2 + 8(2) + 5

= -0.5(16) + 4(8) - 10(4) + 16 + 5

= -8 + 32 - 40 + 16 + 5

= 5 mg/hr

Therefore, the rate of homeglobin production at t = 2 hours is 5 mg/hr.