A travel mug of 90∘C coffee is left on the roof of a parked car on a cold winter day. The temperature of the coffee t minutes after it was left on the roof is given by H(t)=90(2)−t/13. After how many minutes will the coffee be only lukewarm (30∘C)?

Question

anonymous · Answer

$$-t/13=\log_{2} (30/90)$$

anonymous · Answer

This is as far as I got ^^

campbell_st · Answer

well you know h(t) = 30

so make the substitution 

so 

$$30 = 90 \times (2)^{-\frac{t}{13}}$$

divide both sides by 90 

$$\frac{1}{3} = (2)^{-\frac{t}{13}}$$

now take the log of both sides of the equation, using log laws for the power

$$\ln(\frac{1}{3}) = -\frac{t}{13} \times \ln(2)$$

hopefully you can now solve for t

campbell_st · Answer

as a tip, don't use base 2 logs... use a log that is easy to calculate with, natural logs or base 10 logs... 

both will give the same answer.

empty · Answer

Yeah if you're good you can leave out the base of your logarithm until you're ready to evaluate it.