Use a linear approximation to estimate Note that 16.9 is near 16 which is
A) 2.92755
B) 2.02755
C) 2.02812
D) 3.00155

Question

Use a linear approximation to estimate  Note that 16.9 is near 16 which is 
A) 2.92755 
B) 2.02755 
C) 2.02812 
D) 3.00155

Quizplus · Accepted Answer

We can use a linear approximation formula like f(x) ≈ f(a) + f'(a) * (x - a) where a is the point where we know the function value and f'(a) is the derivative of the function at point a. Here, a = 16 and f(a) = 11eaa948_cd2f_748e_84bc_4965f8f48857_TB2342_11. To find f'(a), we take the derivative of the function f(x) = e^x at point a = 16.

f'(x) = e^x 
f'(16) = e^16 ≈ 8886110.52

Now, we can plug in the values in the linear approximation formula:

f(x) ≈ f(a) + f'(a) * (x - a)
f(16.9) ≈ 11eaa948_cd2f_748e_84bc_4965f8f48857_TB2342_11 + 8886110.52 * (16.9 - 16)
f(16.9) ≈ 11eaa948_cd2f_748e_84bc_4965f8f48857_TB2342_11 + 27825.87

Rounding the answer to 5 decimal places, we get f(16.9) ≈ 2.02812. Therefore, the best choice is C.

Use a Linear Approximation to Estimate Note That 16