Question

If dy/dt = 6e⁻⁰.⁰⁸ ⁽ᵗ⁻⁵⁾², by how much does y change as t changes from t=1 to t=6 ?

(A) 3.870
(B) 8.341
(C) 18.017
(D) 22.583

Answer 1

To find how much y changes as t changes from t=1 to t=6, integrate the given expression of dy/dt with respect to t and evaluate the result. The correct answer is B. 8.341.

Step-by-step explanation:

To find how much y changes as t changes from t=1 to t=6, we need to integrate the given expression of dy/dt with respect to t. Here is the step-by-step process:

1. Integrate 6e-0.08(t-5)² with respect to t.
2. Apply the power rule of integration to the exponent and multiply by the derivative of the exponent.
3. Integrate e-0.08(t-5)² and multiply by the constant coefficient (6).
4. Evaluate the integral from t=1 to t=6.
5. Substitute the upper limit (t=6) into the integral and subtract the result when substituting the lower limit (t=1).
6. Simplify the expression to get the change in y.
7. Compare the result with the options provided to determine the correct answer.

The correct option is (B) 8.341.