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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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The temperature inside a certain industrial machine at time t seconds
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31 Mar 2021, 22:23
31 Mar 2021, 22:23
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Question Stats:
50% (01:28) correct
50% (01:24) wrong based on 4 sessions
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The temperature inside a certain industrial machine at time t seconds after startup, for 0 < t < 10, is given by h(t) = \(4^{(2t+1)} – 4^{(t+2)}\) degrees Celsius. How many seconds after startup is the temperature inside the machine equal to 128 degrees Celsius?
(A) 3/2
(B) 2
(C) 5/2
(D) 3
(E) 7/2
(A) 3/2
(B) 2
(C) 5/2
(D) 3
(E) 7/2
Re: The temperature inside a certain industrial machine at time t seconds
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01 Apr 2021, 12:44
01 Apr 2021, 12:44
1
temperature is calculated based on the equation, h(t) = 4^(2t+1) – 4^(t+2)
To avoid complex calculation let's assume our answer is B means t = 2. now plug the value on the equation.
h(t) = 4^(2 * 2 + 1) – 4^(2 + 2)
h(t) = 4^5 - 4^4
h(t) = 4^4 (4 - 1) = 256 * 3 = 768
We are looking for 128 here but got 768 which is way too high, which means we need to choose t < 2. The only option available t < 2 is t = 3 / 2, So it is safe to assume at this point that answer is A. You can also plug the t = 3 / 2 on the equation, you will get h(t) = 128.
To avoid complex calculation let's assume our answer is B means t = 2. now plug the value on the equation.
h(t) = 4^(2 * 2 + 1) – 4^(2 + 2)
h(t) = 4^5 - 4^4
h(t) = 4^4 (4 - 1) = 256 * 3 = 768
We are looking for 128 here but got 768 which is way too high, which means we need to choose t < 2. The only option available t < 2 is t = 3 / 2, So it is safe to assume at this point that answer is A. You can also plug the t = 3 / 2 on the equation, you will get h(t) = 128.
gmatclubot
Re: The temperature inside a certain industrial machine at time t seconds [#permalink]
01 Apr 2021, 12:44
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