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3 years ago

9

three adults and four children must pay $107. two adults and three children must pay $76. find the price of the adult ticks and

the price of a childs ticket

1 answer:

jenyasd209 [6]3 years ago

8 0

Assigning "a" as cost of adult tickets and "c" the cost of children's tickets.

3a + 4c = 107
2a + 3c = 76

elimination method
2(3a + 4c = 107)
-3(2a + 3c = 76)

6a + 8c = 214
-6a - 9c = -228
----------------------
0 - c = - 14
c = 14

Then 2a + 3(14) = 76
2a = 76 - 42
2a = 34
a = 34/2
a = 17

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Uninhibited growth can be modeled by exponential functions other than A(t) =Upper A 0 e Superscript kt. For example, if an i

laila [671]

The question is incomplete. Here is the complete question.

Uninhibited growth can be modeled by exponential functions other than $A(t)=A_{0}e^{kt}$ . for example, if an initial population P₀ requires n units of time to triple, then the function $P(t)=P_{0}(3)^{\frac{t}{n} }$ models the size of the population at time t. An insect population grows exponentially. Complete the parts a through d below.

a) If the population triples in 30 days, and 50 insects are present initially, write an exponential function of the form $P(t)=P_{0}(3)^{\frac{t}{n} }$ that models the population.

b) What will the population be in 47 days?

c) When wil the population reach 750?

d) Express the model from part (a) in the form $A(t)=A_{0}e^{kt}$ .

Answer: a) $P(t)=50(3)^{\frac{t}{30} }$

b) P(t) = 280 insects

c) t = 74 days

d) $A(t)=50e^{0.037t}$

Step-by-step explanation:

a) n is time necessary to triple the population of insects, i.e., n = 30 and P₀ = 50. So, Exponential equation for growth is

$P(t)=50(3)^{\frac{t}{30} }$

b) In t = 47 days:

$P(t)=50(3)^{\frac{t}{30} }$

$P(47)=50(3)^{\frac{47}{30} }$

$P(47)=50(3)^{1.567}$

P(47) = 280

In 47 days, population of insects will be 280

c) P(t) = 750

$750=50(3)^{\frac{t}{30} }$

$\frac{750}{50}=(3)^{\frac{t}{30} }$

$(3)^{\frac{t}{n} }=15$

Using the property <u>Power</u> <u>Rule</u> of logarithm:

$log(3)^{\frac{t}{30} }=log15$

$\frac{t}{30}log(3)=log15$

$t=\frac{log15}{log3} .30$

t = 74

To reach a population of 750 insects, it will take 74 days

d) To express the population growth into the described form, determine the constant k, using the following:

A(t) = 3A₀ and t = 30

$A(t)=A_{0}e^{kt}$

$3A_{0}=A_{0}e^{30k}$

$3=e^{30k}$

Use Power Rule again:

$ln3=ln(e^{30k})$

$ln3=30k$

$k=\frac{ln3}{30}$

k = 0.037

Equation for exponential growth will be:

$A(t)=50e^{0.037t}$

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3 years ago

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The surface area of a shape is the amount of space on the shape

When the dimensions are quadrupled, the new surface area would be 16 times the initial surface area

<h3>How to determine the surface area</h3>

The surface area of a rectangular prism is:

$S = 2 * (lw + lh + wh)$

When quadrupled, we have:

$S_2 = 2 * (16lw + 16lh + 16wh)$

Factor out 16

$S_2 =16 * 2 * (lw + lh + wh)$

Substitute $S = 2 * (lw + lh + wh)$

$S_2 =16 * 2 * S$

The above means that:

The new surface area would be 16 times the initial surface area

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Answer:

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The formula for median depends on the number of values in the dataset.

First of all we have to arrange the given data in order

So,

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Counting the values in the dataset

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As the number of values is even, the formula for median will be

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Putting the values

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vagabundo [1.1K]

you need the ratio of the scale to find the answer.

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