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Ymorist [56]
3 years ago
14

A rabbit population doubles every 4 weeks. There are currently five rabbits in a restricted area. If t represents the time, in w

eeks, and p(t) is the population of rabbits with respect to time, about how many rabbits will be there in 98 days?
Mathematics
1 answer:
Mumz [18]3 years ago
6 0
98 days = (98 ⁄ 7) weeks = 14 weeks 

<span>Po = initial population = 5 </span>

<span>Ƭ = doubling time in weeks </span>

<span>t = elapsed time in weeks </span>

<span>P{t} = population after "t" weeks </span>


<span>    P{t} = (Po)•2^(t ⁄ Ƭ) </span>

<span>    P{t} = (Po)•2^(t ⁄ 4) </span>

<span>    P{t} = 5•2^(t ⁄ 4) </span>

<span>    P{14} = (5)•2^(14 ⁄ 4)   …   t = 14 weeks = 98 days </span>

<span>    P{14} = 56   …   population after 14 weeks</span>
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The slope-intercept form: y = mx + b

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y = 5x + 2 and y = 5x – 8

m = 5                 m = 5

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When comparing equations:

1. Put in <u>slope-intercept</u> form.

2. Compare the <u>slopes and the y-intercepts</u>!

This system has <u>no solution.</u>

Because we have the same slopes and different y-intercepts.

If the slopes are the same and the y-intercepts are the same, then that system has infinitely many solutions.

If the slopes are different, then that system has one solution.

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jasenka [17]
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8 0
2 years ago
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Hot dogs come in packages of 10 and hot dog buns come in packages of 8 . What is the least amount of product that you need to Bu
lubasha [3.4K]

This exercise is solved by finding the least common multiple between 10 and 8.


In fact, you have to buy a certain number h of hot dog package, and you will have 10h hot dogs, since there are 10 hot dogs in each package. The key concept here is that the number of hot dogs you have in the end is a multiple of the number of hot dogs in each box.


Similarly, you have to buy a certain number b of hot dog buns package, and you will have 8b hot dogs, since there are 8 hot dog buns in each package. Again, the key concept here is that the number of hot dog buns you have in the end is a multiple of the number of hot dog buns in each box.


Then, you want to have the same number of hot dogs and hot dog buns, i.e. you want


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but you also want h and b to be the first values to satisfy this equation.


This means that you want a multiple of 10 to equal a multiple of 8, and you want the smallest possible number which does the trick. Again, this is exactly the definition of the least common multiple.


To find the least common multiple of two numbers, find their prime factorization, and collect all the primes from both factorizations, with the highest exponent possible. Since 10 = 2\cdot 5 and 8 = 2^3, the primes appearing are 2 and 5. The higher exponent for 2 is 3, and the only exponent for 5 is 1. So, the answer is 2^3\cdot 5 = 40.


So, if you buy 4 packages of hot dogs and 5 packages of hot dog buns, you will have 40 hot dogs and 40 hot dog buns, as requested.

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3 years ago
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ivolga24 [154]
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Hope this helps!
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