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Natali [406]
4 years ago
13

And international calling plan charges a rate per minute plus a flat fee. A 10 minute call to France costs $4.29. Right and solv

e a linear equation to find the cost of a 12 minute call to France
Mathematics
1 answer:
scZoUnD [109]4 years ago
5 0

Answer:

The cost of a 12 minute call to France is $ 3.63

Step-by-step explanation:

given:

The cost of 15 minute call to France = $ 4.29

The cost of 10 minute call to France   = $ 3.19

To Find :

The cost of a 12 minute call to France = ?

Solution:

Let the flat fee be X

and the cost per minute be Y

so the  15 minute call to France will be

X + 15(Y) = 4.29---------------------------(1)

the  10 minute call to France will be

X + 10(X) = 3.19----------------------------(2)

Subtracting (2) from (1)

X + 15(Y) = 4.29

X + 10(Y) = 3.19

-      -           -

---------------------------------

      5Y = 1.10

--------------------------------

Y =\frac{1.10}{5}

Y = 0.22

So the cost per minute of a call = $0.22

substituting the values in (1)

X + 15(0.22) = 4.29

X + 3.3 = 4.29

X = 4.29 -3.3

X = 0.99

Now the cost of 12 minute call is

=>X + 12(Y)

=> 0.99 + 12(0.22)

=> 0.99 + 2.64

=> 3.63

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Answer:

(a) y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

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Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

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The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

y = a \cdot (1 + r)^t

Plugging in the values, we get;

800,000 = 350,000 \times (1 + r)^{12}

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The  model is therefore;

y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

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By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour =  r × 100

∴   The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

2 \cdot y = y \times (1 + 0.07132)^t

Therefore, we have;

2·y/y =2 = (1 + 0.07132)^t

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

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