(2y4 + 3) - (9 - 5y3

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.

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

$0.5=e^{(24.5)r}$

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 $A=6000e^{-0.23t}$

5 0

3 years ago

Solve the equation x/4 - 7 = y for x

expeople1 [14]

Answer:

x = 4y + 28

Step-by-step explanation:

x/4 - 7 = y

+7 +7

x/4 = y + 7

× 4 × 4

x = 4y + 28

7 0

3 years ago

Read 2 more answers

A spinner has three sections. The table shows the results of spinning the arrow on the spinner 80 times.

AnnyKZ [126]

Answer:

7/20

Step-by-step explanation:

Frequency of Section 1 is 28 and total number of frequencies is 80.

P(Section 1) = 28/80 = 7/20

8 0

2 years ago

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Jonathan weighs thirty pounds more than three times his son Aidan's weight.Their combined weight is 210 pounds.Write an equation

aalyn [17]

The equation should be
j = 30 + 3a
j + a = 210

Solving the equation
j + a = 210
(30 + 3a) + a = 210
30 + 4a = 210
4a = 180
a = 45

j = 30 + 3a
j = 30 + 3 × 45
j = 30 + 135
j = 165

Aiden's weight is 45 pounds, Jonathan's weight is 165 pounds

8 0

3 years ago

Read 2 more answers

consider this quadratic equation x2+2x+7=21 the nuber of positive solutions to this equation are blank. the approximate value of

S_A_V [24]

Answer:

x²+2x+7-21=0

 x²+2x-14. =0

 x²+2x. =14

 x²+2x+1. =14+1

 (X+1)². =15

 X+1. =+/-√15

 X=-1+/-√15

X=-1+3.872983346207

 =2.872983346207(greatest solution) round it as possible

X=-1-3.872983346207

 =-4.872983346207

6 0

3 years ago

(2y4 + 3) - (9 - 5y3 - 6y4)