MATHEMATICS HIGH SCHOOL

For the following exercises, use this scenario: A biologist recorded a count of 360 bacteria present in a culture after 5 minutes and 1000 bacteria present after 20 minutes. Rounding to six significant digits, write an exponential equation representing this situation. To the nearest minute, how long did it take the population to double

Answers

Answer 1

Answer:

Answer:

$P(t)=256*e^(0.068185t)$

10 minutes for the population to double.

Step-by-step explanation:

The general formula for the population equation, P(t), is:

$P(t)=A*e^(nt)$

We are given that for t =5 minutes and t = 2 minutes:

$P(5)=360=A*e^(5n)\nP(20)=1,000=A*e^(20n)\n\n$

Solving for A and n:

$ln(360)=ln(A)+5n\nln(1,000)=ln(A)+20n\nln(1,000)-4ln(360)=ln(A)-4ln(A)+20n-20n\nln(A)=5.5455536\nA=256\nn=(ln(360)-ln(256))/(5)\nn=0.068185$

The exponential equation that represents this situation is:

$P(t)=256*e^(0.068185t)$

The population will double when P(t) = 512 bacteria:

$512=256*e^(0.068185t)\nln(2)=0.068185t\nt=10.17\ minutes$

To the nearest minute, it takes roughly 10 minutes for the population to double.

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What property does the statement show? ( 4 x 8 ) x 3 = ( 4 x 4 ) x 3

Answers

Answer: Associative property of multiplication.

Step-by-step explanation:

The property demonstrated by the statement "(4 x 8) x 3 = (4 x 4) x 3" is the associative property of multiplication.

The associative property of multiplication states that you can change the grouping of numbers in a multiplication expression without changing the result. In this case, both sides of the equation involve multiplication, and the numbers being multiplied are grouped differently but still yield the same result.

commutative property of multiplication

What is the discount of a baseball hat that is $34 with a 28% discount?

Answers

Answer:

12 bucks

Step-by-step explanation:

Charles can do a job in 1 hour, Bill can do the same job in 2 hours, and Bob can do the jobin 3 hours. How long does it take them to do the job working together?

Answers

1hr +2hr+3hr is 6 hours job done

1+2+3=6 hours
bill Charles and bob

If the time is 4:25 am what is the time that is 9 hours and 40 minutes before the time is shown

Answers

Count 9 hours back. 4:25am - 9 hours = 7:25pm.
Count 40 minutes back. 7:25pm - 40 minutes = 6:45pm.
Answer = 6:45pm

Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds. Let p represent the number of pounds of peanuts needed to make the new mixture, and let m represent the number of pounds of the 80% almond-20% peanut mixture. What is the system that models this situation?

Which of the following is a solution to the system: 2 lb peanuts and 3 lb mixture; 2.5 lb peanuts and 2.5 lb mixture; 4 lb peanuts and 1 lb mixture? Show your work.

Answers

Answer: The system that models this situation is:

{p+m=50.6p+0.2m=0.6×5

This system can be solved by substitution or elimination. One possible solution is:

Multiply the second equation by 5 to eliminate the fractions:

{p+m=53p+m=15

Subtract the first equation from the second equation to eliminate m:

2p=10

Solve for p:

p=210=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Another possible solution is:

Multiply the first equation by -0.2 to eliminate m:

{−0.2p−0.2m=−10.6p+0.2m=3

Add the two equations to eliminate m:

0.4p=2

Solve for p:

p=0.42=5

Substitute p into the first equation to find m:

m=5−p=5−5=0

The solution is (p, m) = (5, 0), which means Delaney needs 5 lb of peanuts and 0 lb of mixture.

Therefore, the only correct option among the given choices is 4 lb peanuts and 1 lb mixture.

The distance in feet that Karina swims in a race is represented by 4d - 4, where is d is the distance for each lap. What is an expression equivalent to 4d - 4?