use a calculator to evaluate the function as indicated. (round your answers to three decimal places.) a(t) =…

use a calculator to evaluate the function as indicated. (round your answers to three decimal places.) a(t) = 100 / (1 + e^(-0.06t)) (a) t = 0 (b) t = 25 (c) t = 35

use a calculator to evaluate the function as indicated. (round your answers to three decimal places.) a(t) = 100 / (1 + e^(-0.06t)) (a) t = 0 (b) t = 25 (c) t = 35

Answer

Explanation:

Step1: Substitute t = 0

Substitute (t = 0) into (A(t)=\frac{100}{1 + e^{-0.06t}}). We get (A(0)=\frac{100}{1 + e^{-0.06\times0}}=\frac{100}{1 + e^{0}}). Since (e^{0}=1), then (A(0)=\frac{100}{1 + 1}=50.000).

Step2: Substitute t = 25

Substitute (t = 25) into (A(t)=\frac{100}{1 + e^{-0.06t}}). We have (A(25)=\frac{100}{1 + e^{-0.06\times25}}=\frac{100}{1 + e^{-1.5}}). Using a calculator, (e^{-1.5}\approx0.2231), so (A(25)=\frac{100}{1 + 0.2231}\approx81.759).

Step3: Substitute t = 35

Substitute (t = 35) into (A(t)=\frac{100}{1 + e^{-0.06t}}). We obtain (A(35)=\frac{100}{1 + e^{-0.06\times35}}=\frac{100}{1 + e^{-2.1}}). Using a calculator, (e^{-2.1}\approx0.1225), so (A(35)=\frac{100}{1+ 0.1225}\approx89.087).

Answer:

(a) 50.000 (b) 81.759 (c) 89.087