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3 years ago

The value of a boat after t years is represented by the function f(t)=11,200(0.93)t

Mathematics

2 answers:

alina1380 [7]3 years ago

7 0

Answer: The initial value of the boat is $11,200.

Step-by-step explanation:

An exponential function is represented by

$y=Ab^x$ , where A is the initial amount , b is the rate of increase or decrease and t is the time period.

The given function is an exponential function which gives the value of a boat after t years

$f(t)=11,200(0.93)^t$

If we put t=0 {initial time}

$f(0)=11,200$

Thus, The initial value of the boat is $11,200.

Inessa [10]3 years ago

4 0

The value of a boat after t years is represented by the function f(t)=11,200(0.93)t

The function has the parts of the initial value of the boat

The percent of increase or decrease of the with time

And how in how many times

The 11,200 represents the intial value of the boat

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Q10 A student wants to raise £100 for charity.

ElenaW [278]

Answer:

He must charge minimum £0.84 for one hot dog.

Step-by-step explanation:

Ingredients cost for hot dogs at the supermarket,

Price of dog sausages tin of 8 = 50p ≈ £0.5

Price of dog bun packs of 6 = 90p ≈ £0.90

Number of tins required for 150 hot dogs = $\frac{150}{8}$ = 6.25

So student will purchase 7 tins.

Cost of 7 tins = 7 × 0.5

= £3.5

Number of dog buns packets required = $\frac{150}{6}$ = 25

Cost of 25 packs = 25 × 0.9

= £22.5

Total cost of the material used for 150 buns = 22.5 + 3.5

= £26.0

Let the selling price of each hot dog = £x

Then selling price of 150 hot dogs = £150x

Students wants the profit = £100

So, Selling price - Cost price = profit

150x - 26 = 100

150x = 126

x = $\frac{126}{150}$

x = £0.84

Therefore, he must charge minimum £0.84 for one hot dog.

8 0

3 years ago

Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.

Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

6 0

3 years ago

PLEASE HELP! We can translate ()=2|−2|−5 to the right 3 units and up 5 units to create (). Write the equation for function g.

alisha [4.7K]

Answer:

$g(x)=2\,|x-5|$

Step-by-step explanation:

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$g(x)=2\,|x-3-2|- 5+ 5\\g(x)=2\,|x-5|+0\\g(x)=2\,|x-5|$

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3 years ago

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Triss [41]

Answer:

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Step-by-step explanation:

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MariettaO [177]

X=1
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2 years ago

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