Question

How do you do this question?

Answer 1

Answer:

C. 1.214

Step-by-step explanation:

P(t) = 2 + 5 tan⁻¹(t/2)

When P(t) = 6, the value of t is:

6 = 2 + 5 tan⁻¹(t/2)

4 = 5 tan⁻¹(t/2)

4/5 = tan⁻¹(t/2)

tan(4/5) = t/2

t = 2 tan(4/5)

t ≈ 2.059

The instantaneous rate of change of P(t) is dP/dt:

dP/dt = 5 / (1 + (t/2)²) × 1/2

dP/dt = 5 / (1 + t²/4) × 1/2

dP/dt = 20 / (4 + t²) × 1/2

dP/dt = 10 / (4 + t²)

At t = 2.059:

dP/dt ≈ 1.214

Here's a graph:

desmos.com/calculator/7leerprg4i