An oven is preheated and then remains at a constant temperature. A potato is pla

Question

An oven is preheated and then remains at a constant temperature. A potato is placed in the oven to bake. Suppose that the temperature T (in degree F) of the potato t minutes later is given by T = 425 - 325(0.97^t). The potato will be considered done when its temperature in anywhere between 260 degree F and 280 degree F. for both parts (a) and (b). (a) During what interval of time would the potato be considered done? T_min tildeequal minutes t_max tildeequal minutes (b) How long does it take for the difference between the potato and oven temperatures to be cut in half? Minutes

Explanation / Answer

Given the temperature of potato at time "t" is given by

T = 425 - 325 (0.97^t)

For potato to have temperature of 260, T =260

Then, 260 = 425 - 325 (0.97^t)

325 (0.97^t) = 425 - 260

325 (0.97^t) = 165

(0.97^t) = 0.5076

Applying logerthem on both sides

log (0.97^t) = log (0.5076)

t * log(0.97) = log (0.5076)

t = log (0.5076) / log (0.97)

t =22.26 minutes.

Similarly for potato to have temperature of 280 ; T = 280

Then 280 = 425 - 325 (0.97^t)

325 (0.97^t) = 425 - 280

  325 (0.97^t) = 145

(0.97^t) = 0.4461

Applying logerthem on both sides

log (0.97^t) = log (0.4461)

t * log(0.97) = log (0.4461)

t = log (0.4461) / log (0.97)

t =26.50 minutes.

Therefore minimum time is 22.26 minutes.

maximum time is 26.50 minutes.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.