Question 1187549: Suppose that someone made a hot pizza, right after taking it out of the oven it had the temperature of 110C°, we can only ingest it, without the risk of it burning us, when it have its temperature equivalent to 40°C. The temperature of the food decreases according to the function: f(t)= 120.2^( - 1.6t)+10, with t being minutes. Once ready, from how long can we ingest it without the risk of getting burned?
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Answer by ikleyn(52776)   (Show Source):
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Suppose that someone made a hot pizza, right after taking it out of the oven it had the temperature of 110C°,
we can only ingest it, without the risk of it burning us, when it have its temperature equivalent to 40°C.
The temperature of the food decreases according to the function: f(t)= 120.2^( - 1.6t)+10, with t being minutes.
Once ready, from how long can we ingest it without the risk of getting burned?
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Write the equation as you read the problem
120*2^(-1.6t) + 10 = 40 degrees of Celsium
Simplify it step by step
120*2^(-1.6t) = 40 - 10
120*2^(-1.6t) = 30
2^(-1.6t) = 30/120
2^(-1.6t) = 1/4
2^(-1.6t) = 2^(-2)
Since the exponents are equal and the bases are equal, we conclude that the degrees/(indexes) are equal
-1.6t = -2
t =  =  = 1.25
ANSWER. The customer should wait 1.25 minutes = 1 minute and 15 seconds.
Solved.
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