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30 Dec 2024, 07:00
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x: 4
k: 2
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
68% (02:07) correct
32%
(02:19)
wrong
based on 717
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The current population y of a certain organism is determined by the formula \(y = x(2^{kt})\), in which x is the organism's initial population, t is the number of hours that the organism's population has been growing, and k is a constant that is associated with the organism's hourly growth rate. The number of organisms after 4 hours is 1,024.
Select a value of x and a value of k that are jointly consistent with the given information. Make only two selections, one in each column.
Select a value of x and a value of k that are jointly consistent with the given information. Make only two selections, one in each column.
| x | k | |
| 1 | ||
| 2 | ||
| 3 | ||
| 4 | ||
| 6 | ||
| 8 |
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Official Answer
x: 4
k: 2
31 Dec 2024, 01:05
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Bismuth83
\(y = x(2^{kt})\)
we are given,
\(y = 1024 = 2^{10}\)
\(t = 4\)
Calculate value of x and k
\(2^{10} = x*(2^{4k})\)
Only 2 values of k are possible as 4k <= 10 ie. k<=2.5
| k | x | |
| 1 | \(2^6\) | Not possible |
| 2 | \(2^2\) | Correct |
Hence, (x, k) = (4, 2)
31 Dec 2024, 07:00
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1. We are given a single data point, t = 4 and y = 1024, so let's plug it in: \(1024 = x(2^{k * 4}) \rightarrow 2^{10} = 2^{4k}x\).
2. Looking at the answer choices tells us that x and k are whole numbers from 1 to 8.
3. For the equation to work, x needs to be a power of 2 and 4k must be in between 1 and 10: \(1 \leq 4k \leq 10 \rightarrow 0.25 \leq k \leq 2.5 \rightarrow k = 1 \ or \ 2\).
4. Let's check both possibilities:
- k = 1. \(2^{10} = 2^{4 * 1}x \rightarrow x = 2^{6} = 64\). However, this isn't an answer choice.
- k = 2. \(2^{10} = 2^{4 * 2}x \rightarrow x = 2^{2} = 4\). This is an answer choice.
5. Our answer will be: x - 4 and k - 2.
2. Looking at the answer choices tells us that x and k are whole numbers from 1 to 8.
3. For the equation to work, x needs to be a power of 2 and 4k must be in between 1 and 10: \(1 \leq 4k \leq 10 \rightarrow 0.25 \leq k \leq 2.5 \rightarrow k = 1 \ or \ 2\).
4. Let's check both possibilities:
- k = 1. \(2^{10} = 2^{4 * 1}x \rightarrow x = 2^{6} = 64\). However, this isn't an answer choice.
- k = 2. \(2^{10} = 2^{4 * 2}x \rightarrow x = 2^{2} = 4\). This is an answer choice.
5. Our answer will be: x - 4 and k - 2.
