The object's temperature after 18.0 minutes is 425.83.
Given that,
An object's temperature cools exponentially after it is removed from a furnace (hot oven).
If its initial temperature is 730°C and it cools at a rate of 2.95% per minute.
We have to determine,
The object's temperature after 18.0 minutes.
According to the question,
The initial temperature is 730°C and it cools at a rate of 2.95% per minute,
The temperature after t minutes is modeled by an exponential function, which has the following format is,
[tex]T(t) = T(0) . (1-r)^t[/tex]
Where T(0) is the initial temperature, and r is the cooling rate, as a decimal.
Then,
T(0) = 730°c and r = 2.95% = 0.0295
Substitute all the values in the equation,
[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}[/tex]
Therefore,
The object's temperature after 18.0 minutes is,
[tex]T(t) = T(0) . (1-r)^t\\\\T(18) = 730 \times (1-0.0295)^{18}\\\\ T(18) = 730 \times 0.5833\\\\T (18) = 425.83[/tex]
Hence, The required value of the object's temperature after 18.0 minutes is 425.83.
To know more about the Exponential function click the link given below.
https://brainly.com/question/16902197
