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Romashka-Z-Leto [24]
3 years ago
14

Determining Exponential Growth and Decay in Exercise, use the given information to write an exponential equation for y. Does the

function represent exponential growth or exponential decay?
dy/dt = -2/3y, y = 20 when t = 0
Mathematics
1 answer:
scZoUnD [109]3 years ago
8 0

Answer:

y=20e^{-\frac{2}{3}t}

Exponential decay

Step-by-step explanation:

We are given that

\frac{dy}{dt}=-\frac{2}{3}y

y=20 when t=0

\frac{dy}{y}=-\frac{2}{3}dt

Taking integration on both sides then we get

lny=-\frac{2}{3}t+C

Using formula  \int \frac{dx}{x}=lnx,\int dx=x

y=e^{-\frac{2}{3}t+C}

Using formula

lnx=y\implies x=e^y

y=e^C\cdot e^{-\frac{2}{3}t}

e^C=Constant=C

y=Ce^{-\frac{2}{3}t}

Substitute y=20 and t=0

20=C

Substitute the value of C

y=20e^{-\frac{2}{3}t}

When t tends to infinity then

\lim_{t\rightarrow\infty}=\lim_{t\rightarrow\infty}20e^{-\frac{2}{3}t}=0

When time increases then the value of function decrease

Hence, the  function is exponential decay.

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Tucker bought a new speaker priced at $45 and the sales tax is 7%. What is the total cost of the speaker after tax?
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The total cost is $41.85


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Which expression is equivalent to 4 (9 + 7)
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8 0
2 years ago
A concrete mix is designed to withstand 3000 pounds per square inch​ (psi) of pressure. The following data represent the strengt
ss7ja [257]

Answer:

Mean = 3640

Mode = 4100

Median = 3830.

Step-by-step explanation:

We are given the following data in the question:

Strength of casts (in psi):

3970,4100,3100,3200,2950,3830,4100,4050,3460

Formula:

Mean = \displaystyle\frac{\text{Sum of all observation}}{\text{Total number of observations}}

\displaystyle\frac{3970+4100+3100+ 3200+ 2950+ 3830+4100+ 4050+ 3460}{9} = \displaystyle\frac{32760} {9} = 3640

Mode is the entry with most frequency. Thus, for the given sample mode = 4100.

Median

Since n = 9 is odd,

Formula:

Median = \displaystyle\frac{n+1}{2}th~term

Data in ascending order:

2950,3100,3200,3460,3830,3970,4050,4100,4100

Median = 5th term = 3830.

7 0
3 years ago
Sean is driving to visit his friend in another state.In the first hour he travels 1/5 of the total distance. In the second hour
lozanna [386]

Answer:

They live 285 miles apart

Step-by-step explanation:

Let the total distance be x miles

Sean is driving to visit his friend in another state. In the first hour he travels 1/5 of the total distance. This means that he drove x/5 in the first hour. In the second hour he travels 34 miles. That means

Total distance driven in the first and second hour is

(x/5 + 34)miles

He still has 194 miles more to go.

Therefore,

The total distance is the sum of the distance travelled in the first and second hour + the remaining distance.

x = x/5 + 34 + 194

x = x/5 + 228

Cross multiplying

5x = x + 1140

4x = 1140

x = 1140/4 = 285 miles

7 0
3 years ago
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