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2 years ago

Can somebody help n explain

Mathematics

1 answer:

horrorfan [7]2 years ago

5 0

Answer:

A) 32

Step-by-step explanation:

I will assume the function is

f(x) = 32 (1.5)^x

This is in the form

y =a b^x

in which a is the initial value, b is the growth rate, x is the time

a =32, which is the initial population

b= 1.5, which means 1.5-1 = .5. which means it grows at a 50% increase

x = number of years

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A newborn child receives a $20,000 gift toward college education from her grandparents. How much will the 20,000 be worth in 17

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Answer:

The amount the $20.000 will be worth in 17 years at compound interest is $65068.443

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Here we have the Principal, P = $20,000.00

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Time , t = 17 years

Number of compounding period per year, m = quarterly = 4

The compound interest can be found from the following formula;

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Therefore, by plugging the values of the equation parameters, we have;

$Amount, \ A = 20000 \left (1 + \frac{0.07}{4} \right )^{4 \times 17} = \$ 65068.443$

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7 0

2 years ago

A tank contains 1600 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 2 L/min, and

goldfiish [28.3K]

Let S(t) denote the amount of sugar in the tank at time t. Sugar flows in at a rate of

(0.04 kg/L) * (2 L/min) = 0.08 kg/min = 8/100 kg/min

and flows out at a rate of

(S(t)/1600 kg/L) * (2 L/min) = S(t)/800 kg/min

Then the net flow rate is governed by the differential equation

$\dfrac{\mathrm dS(t)}{\mathrm dt}=\dfrac8{100}-\dfrac{S(t)}{800}$

Solve for S(t):

$\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{S(t)}{800}=\dfrac8{100}$

$e^{t/800}\dfrac{\mathrm dS(t)}{\mathrm dt}+\dfrac{e^{t/800}}{800}S(t)=\dfrac8{100}e^{t/800}$

The left side is the derivative of a product:

$\dfrac{\mathrm d}{\mathrm dt}\left[e^{t/800}S(t)\right]=\dfrac8{100}e^{t/800}$

Integrate both sides:

$e^{t/800}S(t)=\displaystyle\frac8{100}\int e^{t/800}\,\mathrm dt$

$e^{t/800}S(t)=64e^{t/800}+C$

$S(t)=64+Ce^{-t/800}$

There's no sugar in the water at the start, so (a) S(0) = 0, which gives

$0=64+C\impleis C=-64$

and so (b) the amount of sugar in the tank at time t is

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As $t\to\infty$ , the exponential term vanishes and (c) the tank will eventually contain 64 kg of sugar.

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3 years ago

The Capacity of a 1 cm cube is 1 mL. How many 1 cm ice cubes do you need to melt to fill a 1.5 L jar.

Svetach [21]

1500 ice cubes need to fill 1.5 L jar

Solution:

1 cm = 1 ml

Capacity of ice cube = 1 cm

= 1 ml

Capacity of jar = 1.5 L

1 L = 1000 ml

1.5 L = 1.5 × 1000

= 1500 ml

Capacity of jar = 1500 ml

$$\text{Number of ice cubes} =\frac{\text{Capacity of ice cube}}{\text{Capacity of jar}}$

$$=\frac{1500}{1}$

= 1500

Therefore 1500 ice cubes need to fill 1.5 L jar.

8 0

2 years ago

Can somebody help n explain ​

Can somebody help n explain