Question

How do you do this question?

Answer 1

C. 1.698

Explanation:

A'(t) = 2 + 9e^(0.4 sin t)

At t = 1.2:

A'(1.2) = 2 + 9e^(0.4 sin 1.2)

A'(1.2) ≈ 15.066

So the slope of the tangent line at (1.2, 7.5) is:

y = 15.066 (x − 1.2) + 7.5

Using this line to approximate A(t), we set y to 15 and solve for x:

15 = 15.066 (x − 1.2) + 7.5

7.5 = 15.066 (x − 1.2)

0.498 = x − 1.2

x = 1.698