`T(x)=(60(1/2)^x)/30 +20`  Where T(x) is the Temp. in Celsius and x is the time elapsed in minutes. How to graph the function;and Time to reach 28 celsius.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to reduce duplicate factors to simplify the equation of the function, such that:

`T(x) = (60*(1/2)^x)/30 + 20 => T(x) = 2*(1/2)^x + 20`

You need to use the negative power property such that:

`T(x) = 2*(2^(-1))^x + 20 => T(x) = 2*2^(-x) + 20`

Using the properties of exponential function yields:

`T(x) = 2*2^(-x) + 20 => T(x) = 2^(1-x) + 20`

You need to evaluate the time elapsed for temperature to reach `28^o C` , hence, you need to substitute `28`  for `T(x)`  in the given equation, such that:

`28 = 2^(1-x) + 20`

You need to isolate the terms that contain x to one side, such that:

`2^(1-x) = 28 - 20 => 2^(1-x) = 8 => 2^(1-x) = 2^` 3

Using the properties of exponential function yields:

`1 - x = 3 => x = -2`

Sketching the graph of the function T(x) = 2^(1-x) + 20 yields:

Hence, evaluating the time elapsed for the temperature to reach `28^o C`  yields `x = 2`  minutes.

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