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riadik2000 [5.3K]

3 years ago

9

Which expression can be used to represent the phrase Lamar decreased his collection of cards by seven

1 answer:

jenyasd209 [6]3 years ago

3 0

Answer:

$x-7$

Step-by-step explanation:

Let

x------> Lamar's collection of cards

The algebraic expression of the phrase "Lamar decreased his collection of cards by seven" is equal to subtract the number seven from Lamar's collection of cards

so

$x-7$

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LekaFEV [45]

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3 years ago

The manager of a national park determines that the park can sustain 81 coyotes. The manager assumes that the rate of change of t

Katena32 [7]

Answer:

$N(T) = \frac{81*40*e^{1.075t}}}{81 + 40*(e^{1.075t} - 1)}$

Step-by-step explanation:

This problem can be solved by the logistic equation of populations, that is:

$N(t) = \frac{KN_{0}e^{rt}}}{K + N_{0}(e^{rt} - 1)}$

In which K is the carrying capacity of the population, $N_{0}$ is the initial population, r is the decimal growth rate and t is the period of time.

In this problem, we have that:

When t = 0, the population is 40: This means that $N_{0} = 40$ .

The manager of a national park determines that the park can sustain 81 coyotes. This means that $K = 81$ .

When t = 1, the population has increased to 60. This means that $N(1) = 60$ .

To write the equation, we have to find the value of r.

$N(t) = \frac{KN_{0}e^{rt}}}{K + N_{0}(e^{rt} - 1)}$

$60 = \frac{81*40*e^{r}}}{81 + 40*(e^{r} - 1)}$

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Now we apply ln to both sides, and:

$r = 1.075$

The answer is:

$N(T) = \frac{81*40*e^{1.075t}}}{81 + 40*(e^{1.075t} - 1)}$

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