Stitz-Zeager_College_Algebra_e-book

410 hooked on conics y 1 x 1 1 1 2 3 the vertex lies

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: , we use the fact that after 2 hours, the roast is 125◦ F, which means T (2) = 125. This gives rise to the equation 350 − 310e−2k = 125 which yields k = − 1 ln 45 ≈ 0.1602. The temperature function is 2 62 T (t) = 350 − 310e 2 ln( 62 ) ≈ 350 − 310e−0.1602t . t 45 384 Exponential and Logarithmic Functions 2. To determine when the roast is done, we set T (t) = 165. This gives 350 − 310e−0.1602t = 165 1 whose solution is t = − 0.1602 ln 37 ≈ 3.22. It takes roughly 3 hours and 15 minutes to cook 62 the roast completely. If we had taken the time to graph y = T (t) in Example 6.5.4, we would have found the horizontal asymptote to be y = 350, which corresponds to the temperature of the oven. We can also arrive at this conclusion by applying a bit of ‘number sense’. As t → ∞, −0.1602t ≈ very big (−) so that e−0.1602t ≈ very small (+). The larger the value of t, the smaller e−0.1602t becomes so that T (t) ≈ 350 − very small (+), which indicates the...
View Full Document

This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

Ask a homework question - tutors are online