The initial temperature difference of 101-45 = 56 degees declined to 101-55 = 46 degrees in 8 minutes, We can write the exponential equation for the soda's temperature as

... T = 101 -56(46/56)^(t/8) . . . . where t is in minutes

After an additional 10 minutes, we have t=18, so the soda temperature will be

... T = 101 -56(46/56)^(18/8) ≈ 65.0 . . . degrees

6 0

3 years ago

Find the Domain of the following exponential and logarithmic equations and solve them:

kakasveta [241]

The base of a logarithm should always be positive and can't be equal to 1, so the domain is 0 < x < 1 or x > 1.

$\log_{\frac1x}243=5$

Write both sides as powers of 1/x :

$\left(\dfrac1x\right)^{\log_{\frac1x}243}=\left(\dfrac1x\right)^5$

Recall that $a^{\log_ab}=b$ , so that

$243=\left(\dfrac1x\right)^5$

$243=\dfrac1{x^5}$

$x^5=\dfrac1{243}$

Take the 5th root of both sides, recalling that 3⁵ = 243, so

$x=\sqrt[5]{\dfrac1{243}}=\boxed{\dfrac13}$

5 0

3 years ago

A store owner will order iPads for local schools. The relationship between x, the number of boxes he will order, and y, the numb

wolverine [178]

Answer:

y, ‎y = ‎15x.

Step-by-step explanation:

7 0

3 years ago

What is 52,566 times 98,173

brilliants [131]

Answer:

5160561918

Step-by-step explanation:

52566 x 98173 = 5160561918

7 0

4 years ago

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