Question

Estimate the relative rate of change of f(t) = 4t at t = 5. Use At = 0.01. Round your answer to two decimal places. The relative rate of change is i Suppose that f(t) is a function with f(25) = 3.4 and f'(25) = -0.5. Estimate f(26) and f(30). f(26) = f(30) =

Answer 1

To estimate the relative rate of change of f(t) = 4t at t = 5 using At = 0.01, we need to calculate the difference quotient:

f'(5) ≈ (f(5 + At) - f(5))/(At)

f'(5) ≈ (f(5.01) - f(5))/(0.01)

Substitute f(t) = 4t into the equation:

f'(5) ≈ (4(5.01) - 4(5))/(0.01)

f'(5) ≈ (20.04 - 20)/(0.01)

f'(5) ≈ 0.04/0.01

f'(5) ≈ 4

Therefore, the relative rate of change of f(t) = 4t at t = 5 is approximately 4.

To estimate f(26), we can use f'(25) ≈ (f(26) - f(25))/(1):

-0.5 ≈ (f(26) - 3.4)/(1)

Solving for f(26):

f(26) ≈ -0.5 + 3.4

f(26) ≈ 2.9

Therefore, f(26) is approximately 2.9.

To estimate f(30), we can use f'(25) ≈ (f(30) - f(25))/(5):

-0.5 ≈ (f(30) - 3.4)/(5)

Solving for f(30):

f(30) ≈ (-0.5)(5) + 3.4

f(30) ≈ -2.5 + 3.4

f(30) ≈ 0.9

Therefore, f(30) is approximately 0.9.