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2 years ago

5

The volume of a landfill doubles every three years. Write an exponential function to represent this.

1 answer:

stellarik [79]2 years ago

7 0

The equation would be: V = A2^(Y/3)

The basic form of an exponential equation is y = ab^x.

The a is the starting amount. In this problem, we don't know that, so we just leave it as a.

The b is the rate. In this case, we are doubling the volume so we times it by 2.

The x is the amount of years. Since it is every 3 years, we can divide the x by 3.

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Verify that P = Ce^t /1 + Ce^t is a one-parameter family of solutions to the differential equation dP dt = P(1 − P).

NemiM [27]

Answer:

See verification below

Step-by-step explanation:

We can differentiate P(t) respect to t with usual rules (quotient, exponential, and sum) and rearrange the result. First, note that

$1-P=1-\frac{ce^t}{1+ce^t}=\frac{1+ce^t-ce^t}{1+ce^t}=\frac{1}{1+ce^t}$

Now, differentiate to obtain

$\frac{dP}{dt}=(\frac{ce^t}{1+ce^t})'=\frac{(ce^t)'(1+ce^t)-(ce^t)(1+ce^t)'}{(1+ce^t)^2}$

$=\frac{(ce^t)(1+ce^t)-(ce^t)(ce^t)}{(1+ce^t)^2}=\frac{ce^t+ce^{2t}-ce^{2t}}{(1+ce^t)^2}=\frac{ce^t}{(1+ce^t)^2}$

To obtain the required form, extract a factor in both the numerator and denominator:

$\frac{dP}{dt}=\frac{ce^t}{1+ce^t}\frac{1}{1+ce^t}=P(1-P)$

3 0

3 years ago

The square of a number is 12 less then 7 times the number. 2hat is the number

Salsk061 [2.6K]

Hello.

The are answer is 4 or 3
<span>

3^2 = 7(3) - 12
9 = 21 - 12
9 = 9

</span>4^2 = 7(4) - 12
16 = 28 - 12
16 = 16

Have a nice day

3 0

2 years ago

f(x)=5x reflected over the x axis

postnew [5]

Answer:

f(x) = -5x

Step-by-step explanation:

Just add a - sign to reflect it over the x axis

6 0

3 years ago

Currently they sell a tub of popcorn for $10. SHOW or EXPLAIN what the cost of the cone of popcorn should be. Door context: The

Nina [5.8K]

Answer:

The cost of cone of popcorn is $ 2.59.

Step-by-step explanation:

The tub has a volume of 540.473 and costs $10. The cone has a volume of 140.035.

The cost of per unit volume is

$10/540.473

The cost of cone of popcorn is

$\frac{10}{540.473}\times 140.035\\\\2.59$

7 0

3 years ago

Write a how many units in 1 group word Problem for 4 divided by 2/3

Nastasia [14]

$\displaystyle\bf\\4:\frac{2}{3}=4\times\frac{3}{2}=\frac{4\times3}{2}=2\times3=6$

4 0

3 years ago