Mathematics, 22.01.2021 18:50 blackeyes7659

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, find the object's temperature after 18.0 minutes.

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Answer from: Ronatalawrence828

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,

= T(t) = T(0).(1-r)^t

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,

$= T(t) = T(0).(1-r)^t\\\\= T(t) = 730 \times (1-0.0295)^t$

Therefore,

The object's temperature after 18.0 minutes is,

$= T(t) = T(0).(1-r)^t\\\\= T(18) = 730 \times (1-0.0295)^{18}\\\\= T(18) = 730 \times 0.5833\\\\ = T(18) = 425.8361$

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.

link

Answer from: brionnashelp

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:

$T(t) = T(0)(1-r)^{t}$

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 T(0) = 730, r = 0.0295 . So

$T(t) = T(0)(1-r)^{t}$

$T(t) = 730(1-0.0295)^{t}$

$T(t) = 730(0.9705)^{t}$

Find the object's temperature after 18.0 minutes.

This is T(18) . So

$T(t) = 730(0.9705)^{t}$

$T(18) = 730(0.9705)^{18} = 426$

The object's temperature after 18 minutes is of 426ºC.

Answer from: Quest

to find the unit price, we must figure out the cost of one item (in this case one dish towel). to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

Answer from: Quest

step-by-step explanation:

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