Answer:
C. 1.698
Step-by-step 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
