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3 years ago

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ANSWER BOTH QUESTIONS

1 answer:

mash [69]3 years ago

5 0

Answer:

a and c

Step-by-step explanation:

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A bacteria culture starts with 12,000 bacteria and the number doubles every 50 minutes.

Vlada [557]

Answer:

a) $y=12000(2)^{\frac{t}{50}}$

b) Approx. 27,569 bacteria

c) About 103 minutes

Step-by-step explanation:

a)

This will follow exponential modelling with form of equation shown below:

$y=Ab^{\frac{t}{n}}$

Where

A is the initial amount (here, 12000)

b is the growth factor (double, so growth factor is "2")

n is the number of minutes in which it doubles, so n = 50

Substituting, we get our formula:

$y=Ab^{\frac{t}{n}}\\y=12000(2)^{\frac{t}{50}}$

b)

To get number of bacteria after 1 hour, we have to plug in the time into "t" of the formula we wrote earlier.

Remember, t is in minutes, so

1 hour = 60 minutes

t = 60

Substituting, we get:

$y=12000(2)^{\frac{t}{50}}\\y=12000(2)^{\frac{60}{50}}\\y=12000(2)^{\frac{6}{5}}\\y=27,568.76$

The number of bacteria after 1 hour would approximate be <u>27,569 bacteria</u>

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c)

To get TIME to go to 50,000 bacteria, we will substitute 50,000 into "y" of the equation and solve the equation using natural logarithms to get t. Shown below:

$y=12000(2)^{\frac{t}{50}}\\50,000=12,000(2)^{\frac{t}{50}}\\4.17=2^{\frac{t}{50}}\\Ln(4.17)=Ln(2^{\frac{t}{50}})\\Ln(4.17)=\frac{t}{50}*Ln(2)\\\frac{t}{50}=\frac{Ln(4.17)}{Ln(2)}\\\frac{t}{50}=2.06\\t=103$

After about 103 minutes, there will be 50,000 bacteria

4 0

3 years ago

Pls help meeeee

Rashid [163]

Answer:

6 gallons of gas

Step-by-step explanation:

20.00 - 2.12 = 17.88

17.88 divided by 2.98 equals 6

8 0

2 years ago

Read 2 more answers

If a number becomes 2.5 times smaller, by what percent was it decreased?

Gwar [14]

Answer: 40%

Step-by-step explanation: 1 Divided by 2.5 is 0.4, or 40%.

4 0

3 years ago

Read 2 more answers

Solve by using Pythagorean Theorem, a= 5, b= x-1, and c=x

charle [14.2K]

The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.

Step-by-step explanation:

The given is,

a = 5

b = x - 1

c = x

Step:1

Pythagorean theorem is,

$a^{2} + b^{2} = c^{2}$ ................................(1)

( It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides )

From the given values the equation (1) becomes,

$5^{2} + (x-1) ^{2} = x^{2}$

( $(a-b)^{2} = a^{2} + b^{2} -2ab$ )

25 + ( $x^{2}$ + 1 - 2x ) = $x^{2}$

25 + 1 -2x = 0 ( ∵ Eliminate $x^{2}$ in both sides)

26 = 2x

x = 13

Step:2

From the values of x,

a = 5

b = ( 13 - 1 ) = 12

c = 13

Result:

The value of x is 13, from the values of x the values of a,b and c becomes 5, 12 and 13, which is obtained by using Pythagorean theorem.

3 0

3 years ago

Regina has just opened her new yarn shop. She makes $4.00 on every skein of yarn sold and her monthly expenses are $3,800. Which

MAXImum [283]

Answer:

31 is prime. and it’s prime factorization is just 31....

Step-by-step explanation:

6 0

2 years ago