Question

use your calculator to find the value of ( f(0.5) ) if ( f(t) = 26.5e^{-0.61t} ). (round your answer to the neare

Explanation:

Step1: Substitute t = 0.5 into the function

We have the function \( f(t)=26.5e^{-0.61t} \). Substitute \( t = 0.5 \) into it, so we get \( f(0.5)=26.5e^{-0.61\times0.5} \).

Step2: Calculate the exponent

First, calculate the exponent part: \( - 0.61\times0.5=-0.305 \). So now the function becomes \( f(0.5)=26.5e^{-0.305} \).

Step3: Calculate the value of \( e^{-0.305} \)

Using a calculator, \( e^{-0.305}\approx0.737 \) (the value can be obtained more accurately by calculator).

Step4: Calculate the final result

Multiply 26.5 by 0.737: \( 26.5\times0.737 = 26.5\times(0.7 + 0.03+0.007)=26.5\times0.7+26.5\times0.03 + 26.5\times0.007=18.55+0.795 + 0.1855 = 19.5305\approx19.53 \) (if we use a more accurate value of \( e^{-0.305}\), for example, if \( e^{-0.305}\approx0.73704 \), then \( 26.5\times0.73704 = 26.5\times0.73704 = 19.53156\approx19.53 \)).

Answer:

\( 19.53 \) (the answer may vary slightly depending on the precision of the calculator used for calculating \( e^{-0.305} \))