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2 years ago

A landscaping company charges $50 per cubic yard of mulch plus a delivery charge of $24. Find a

Mathematics

1 answer:

Zigmanuir [339]2 years ago

5 0

Answer: c(x) = $50*x + $24

Step-by-step explanation:

First, this situation can be modeled with a linear equation like:

c(x) = s*x + b

where c is the cost, s is the slope, x is the number of cubic yards of mulch bought, and b is the y-intercept ( a constant that no depends on the number x)

Then we know that:

The company charges $50 per cubic yard, so the slope is $50

A delivery charge of $24, this delivery charge does not depend on x, so this is the y-intercept.

Then our equation is:

c(x) = $50*x + $24

This is:

"The cost of buying x cubic yards of mulch"

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stiv31 [10]

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2 years ago

A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

serious [3.7K]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

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After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

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3 years ago

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bixtya [17]

Answer:

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Step-by-step explanation:

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2 years ago

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Step-by-step explanation:

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3 years ago

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3 years ago