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anyanavicka [17]

3 years ago

12

In 2000 the population of a small village was 2,400. With an annual growth rate of approximately 1.68%, compounded continuously,

what will the population be in 2020 according to the exponential growth function?

1 answer:

Triss [41]3 years ago

3 0

Answer:

$3,358\ people$

Step-by-step explanation:

The formula to calculate the exponential growth function is equal to

$f(x)=P(e)^{rx}$

where

f(x) is the population

P is the population in the year 2000

r is the rate in decimal

x is number of years since 2000

e is the mathematical constant number

we have

$x=2020-2000=20\ years\\ P=2,400\\ r=0.0168$

substitute in the formula above

$f(x)=2,400(e)^{0.0168*20}$

$f(x)=3,358\ people$

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maxonik [38]

Answer with Step-by-step explanation:

We are given that

$r(t)=< t^2,\frac{2}{3}t^3,t >$

We have to find T,N and B at the given point t > (1, $2/3$ ,1)

$r'(t)=$

$\mid r'(t) \mid=\sqrt{(2t)^2+(2t^2)^2+1}=\sqrt{(2t^2+1)^2}=2t^2+1$

$T(t)=\frac{r'(t)}{\mid r'(t)\mid}=\frac{}{2t^2+1}$

Now, substitute t=1

$T(1)=\frac{}{2+1}=\frac{1}{3}$

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$T'(1)=-\frac{4}{9}+\frac{1}{3}$

$T'(1)=\frac{1}{9}=$

$\mid T'(1)\mid=\sqrt{(\frac{-2}{9})^2+(\frac{4}{9})^2+(\frac{-4}{9})^2}=\sqrt{\frac{36}{81}}=\frac{2}{3}$

$N(1)=\frac{T'(1)}{\mid T'(1)\mid}$

$N(1)=\frac{}{\frac{2}{3}}=$

$N(1)=$

$B(1)=T(1)\times N(1)$

$B(1)=\begin{vmatrix}i&j&k\\\frac{2}{3}&\frac{2}{3}&\frac{1}{3}\\\frac{-1}{3}&\frac{2}{3}&\frac{-2}{3}\end{vmatrix}$

$B(1)=i(\frac{-4}{9}-\frac{2}{9})-j(\frac{-4}{9}+\frac{1}{3})+k(\frac{4}{9}+\frac{2}{9})$

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$B(1)=\frac{1}{3}$

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Rom4ik [11]

Answer:

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Meaning: If the company sells -5 shirts, they would make a profit of -150 dollars. This interpretation of loss in the context of the problem

$f(7) = -30$

Meaning: If the company sells 7 shirts, they would make a profit of -30 dollars. This interpretation of loss in the context of the problem

$f(10.5) = 5$

Meaning: If the company sells 10.5 shirts, they would make a profit of 5 dollars. This interpretation of profit in the context of the problem

Step-by-step explanation:

Given

$f(x) = 10x - 100$

Required

Fill in the gap

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$f(-5) = -50 -100$

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$f(10.5) = 105 - 100$

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vesna_86 [32]

Answer:

1. Trapezoid

2. Kite

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Step-by-step explanation:

Given - Use the properties of quadrilaterals to complete the statements.

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A ....... must have two pairs of adjacent sides congruent.

A ........ must have all congruent sides.

Proof -

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A Square, Rhombus must have all congruent sides.

Reason -

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A kite is a quadrilateral with exactly two pairs of adjacent congruent sides.

A rhombus is a parallelogram with four congruent sides.

A square can be defined as a rhombus which is also a rectangle . In other words, a square is a parallelogram with four congruent sides and four right angles.

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Answer:

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Step-by-step explanation:

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8 0

3 years ago