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4 years ago

Identifiy the initial amount a and the decay factor b in the exponential function y=5×0.5^×

Mathematics

1 answer:

xenn [34]4 years ago

6 0

Answer:

$a=5\\ \\b=0.5$

Step-by-step explanation:

Given the exponential decay function $y=5\cdot (0.5)^x$

When $x=0,$ then

$y=5\cdot (0.5)^0=5\cdot 1=5,$

so the initial amount is $a=5$

The exponential decay function $y=a\cdot b^x$ has the decay factor $b.$

In your case, the eexponential decay factor is $b=0.5$

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olga55 [171]

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3 years ago

Suppose that a spherical droplet of liquid evaporates at a rate that is proportional to its surface area: where V = volume (mm3

Alex

Answer:

V = 20.2969 mm^3 @ t = 10

r = 1.692 mm @ t = 10

Step-by-step explanation:

The solution to the first order ordinary differential equation:

$\frac{dV}{dt} = -kA$

Using Euler's method

$\frac{dVi}{dt} = -k *4pi*r^2_{i} = -k *4pi*(\frac {3 V_{i} }{4pi})^(2/3)\\ V_{i+1} = V'_{i} *h + V_{i} \\$

Where initial droplet volume is:

$V(0) = \frac{4pi}{3} * r(0)^3 = \frac{4pi}{3} * 2.5^3 = 65.45 mm^3$

Hence, the iterative solution will be as next:

i = 1, ti = 0, Vi = 65.45

$V'_{i} = -k *4pi*(\frac{3*65.45}{4pi})^(2/3) = -6.283\\V_{i+1} = 65.45-6.283*0.25 = 63.88$

i = 2, ti = 0.5, Vi = 63.88

$V'_{i} = -k *4pi*(\frac{3*63.88}{4pi})^(2/3) = -6.182\\V_{i+1} = 63.88-6.182*0.25 = 62.33$

i = 3, ti = 1, Vi = 62.33

$V'_{i} = -k *4pi*(\frac{3*62.33}{4pi})^(2/3) = -6.082\\V_{i+1} = 62.33-6.082*0.25 = 60.813$

We compute the next iterations in MATLAB (see attachment)

Volume @ t = 10 is = 20.2969

The droplet radius at t=10 mins

$r(10) = (\frac{3*20.2969}{4pi})^(2/3) = 1.692 mm\\$

The average change of droplet radius with time is:

Δr/Δt = $\frac{r(10) - r(0)}{10-0} = \frac{1.692 - 2.5}{10} = -0.0808 mm/min$

The value of the evaporation rate is close the value of k = 0.08 mm/min

Hence, the results are accurate and consistent!

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3 years ago

Answer For Brainliest

liq [111]

Answer:

the answer is D

Step-by-step explanation:

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3 years ago

I really need help ASAP !!

Vesnalui [34]

Answer:

Graph 1: Consistent Dependent

Graph 2: Consistent Independent

Graph 3: Consistent Dependent

Graph 4: Inconsistent

Step-by-step explanation:

Consistent means they have at least one solution. So lines that intersect once or lines that intersect infinitely many times are both consistent systems.

If they are the system that has one solution they are considered independent.

If they are the system that has infinitely many solutions then are considered dependent.

Inconsistent means they won't intersect at all.

First graph shows the same line graphed onto itself. That means they have infinitely many solutions and is therefore a consistent dependent system.

Second graph shows the lines intersecting once. That means they have one solution and therefore is a consistent independent system.

Third graph shows the same description of graph one and is therefore a consistent dependent system.

The last graph shows parallel lines. Parallel lines do not intersect and therefore do not have a solution. So this system is inconsistent.

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3 years ago

Please help and tell me how to do this <br> 20 POINTS

svp [43]

The answers are :
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16) -300

17) -276
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3 years ago

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