Answer:
option 4. The graph has zeroes at x = 15 an x = -15 and it opens upward.
Step-by-step explanation:
we have
This is the equation of a vertical parabola open upward (the leading coefficient is positive)
The vertex represent a minimum
The vertex is the point (0,-225)
The axis of symmetry is x=0 (y-axis)
Find the x-intercepts (values of x when the value of y is equal to zero)
For y=0
square root both sides
therefore
The graph has zeroes at x = 15 an x = -15 and it opens upward.
Answer:
110.5348 minutes
Step-by-step explanation:
The difference from room temperature changes from 103 to 59 in 46 minutes, so that difference can be modeled by the exponential equation ...
Δt = 103×(59/103)^(t/46)
We want to find t for the temperature difference Δt = 91 -64 = 27.
27 = 103×(59/103)^(t/46)
27/103 = (59/103)^(t/46) . . . . . divide by 103
Taking logs gives the linear equation ...
log(27/103) = (t/46)log(59/103)
Multiplying by the inverse of the coefficient of t, we get ...
t = 46·log(27/103)/log(59/103) ≈ 46·(-0.58147346)/(-0.24198521)
≈ 110.5347
It will take about 110.5347 minutes for the turkey to cool to 91 °F internally.
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<em>Comment on 4 decimal places</em>
An answer correct to 4 decimal places (7 significant digits) is a pretty good indication that the problem was worked correctly. However, that level of precision in the timing makes little sense in this context. Most thermometers will take at least a few seconds to register the temperature to within a tenth of a degree or so. This problem is asking for an answer that is within 6 milliseconds and 30 micro-degrees. Neither of these is anywhere near realistic for a kitchen meat thermometer.
More realistic would be an answer to 4 <em>significant figures</em>, a tenth of a minute and a few hundredths of a degree.
(The rate of change at the time of interest is about -0.33 degrees per minute.)
