Mathematics, 06.03.2020 18:56 eriksprincess13

The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 25% in 10 years. What will be the population in 40 years

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Answer from: MK100

The population in 40 years will be 1220.

Step-by-step explanation:

The population of a town grows at a rate proportional to the population present at time t.

This means that:

$P(t) = P(0)e^{rt}$

In which P(t) is the population after t years, P(0) is the initial population and r is the growth rate.

The initial population of 500 increases by 25% in 10 years.

This means that P(0) = 500, P(10) = 1.25*500 = 625

We apply this to the equation and find t.

$P(t) = P(0)e^{rt}$

$625 = 500e^{10r}$

$e^{10r} = \frac{625}{500}$

$e^{10r} = 1.25$

Applying ln to both sides

$\ln{e^{10r}} = \ln{1.25}$

$10r = \ln{1.25}$

$r = \frac{\ln{1.25}}{10}$

r = 0.0223

$P(t) = 500e^{0.0223t}$

What will be the population in 40 years

This is P(40).

$P(t) = 500e^{0.0223t}$

$P(40) = 500e^{0.0223*40} = 1220$

The population in 40 years will be 1220.

Answer from: Quest

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

Answer from: Quest

option: d is the correct answer.

d) none of the above.

step-by-step explanation:

clearly from the figure attached to the question we could see that there is no shape given. hence without any shape given in the figure and after rotation we can't obtained a square pyramid.

since, to obtain a image we need a proper figure of the pre-image so that it can be transformed.

hence, the correct answer is:

d) none of the above.

step-by-step explanation:

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