Show work and give a numerical answer for full credit. 1. Given the function est

Question

Show work and give a numerical answer for full credit. 1. Given the function estimate the value of aniusing the value h 0.001. Round to two decimal places sing the value h 0.01 Given estimate the value of Round to two decimal places 3. The population of a small country can be modeled by the exponential function se where Pis measured in millions and tis measured in years. Using the value h 0.1.estimate the rate of change of the population in 10 years. Round to two decimal places. 4. Use the graph below to determine the sign (negative, zero, positive) f (C)

Explanation / Answer

1)

f(2) = 2^2 - 4(2) + 1 = -3
f(2.001) = 2.001^2 - 4(2.001) + 1 = -2.999999

(f(2.001) - f(2)) / (2.001 - 2)
(-2.999999 - (-3)) / 0.001
0.001

2)

f(x) = 2^x
f(3) = 2^3 =8

f(3.01) = 2^(3.01) = 8.0556444

(f(3.01) - f(3)) / (3.01 - 3)
(8.0556444 - 8) / 0.01
5.56 approx

3)

P(t) = 5*e^(0.02t)
P(10) = 5e^(0.02*10) = 6.1070137908
P(10.1) = 5e^(0.02*10.1) = 6.11924004

(6.11924004 - 6.1070137908) / (10.1 - 10)
0.12 --> ANSWER

4)

f'(E) = positive because at that point the graph of the function, F is going upward
f'(H) = 0(local minima)
f'(B) = 0(local maxima)
f'(C) = negative

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