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Dafna11 [192]
3 years ago
10

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

exponential function that represents the size of the bacteria population after t hours.
Mathematics
1 answer:
tester [92]3 years ago
4 0

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)}

0.5=e^{(24.5)r}

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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Lina20 [59]

Answer:

-7x + 14 = 56

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-7x = 42

Divide both sides by -7

(-7x)/(-7) = 42/(-7)

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3 0
3 years ago
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Step-by-step explanation:

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6 0
3 years ago
Which of the following accurately lists all discontinuities of the function below?
jeka94
Checking the <span>discontinuity at point -4
from the left f(-4) = 4
from the right f(-4) = (-4+2)² = (-2)² = 4
∴ The function is continues at -4
</span>
<span>Checking the <span>discontinuity at point -2
from the left f(-2) = </span></span><span><span>(-2+2)² = 0
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</span>
<span>Checking the <span>discontinuity at point 4
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