Respuesta :
Answer:
The object's temperature after 18 minutes is of 426ºC.
Step-by-step explanation:
The temperature after t minutes is modeled by an exponential function, which has the following format:
[tex]T(t) = T(0)(1-r)^{t}[/tex]
In which T(0) is the initial temperature, and r is the cooling rate, as a decimal.
Its initial temperature is 730°C and it cools at a rate of 2.95% per minute
This means that [tex]T(0) = 730, r = 0.0295[/tex]. So
[tex]T(t) = T(0)(1-r)^{t}[/tex]
[tex]T(t) = 730(1-0.0295)^{t}[/tex]
[tex]T(t) = 730(0.9705)^{t}[/tex]
Find the object's temperature after 18.0 minutes.
This is [tex]T(18)[/tex]. So
[tex]T(t) = 730(0.9705)^{t}[/tex]
[tex]T(18) = 730(0.9705)^{18} = 426[/tex]
The object's temperature after 18 minutes is of 426ºC.
The required value of 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,
Find 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(t) = 730 \times (1-0.0295)^t[/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) = 425.8361[/tex]
Hence, The required value of the object's temperature after 18.0 minutes is 425.83.
To know more about Exponential Function click the link given below.
https://brainly.com/question/25678010
