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vampirchik [111]
3 years ago
13

suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A samp

le of 1700 bacteria selected from this population reach the size of 1892 bacteria in three hours. Find the hourly growth rate parameter
Mathematics
1 answer:
Tema [17]3 years ago
8 0

Answer:

3.33% per hour

Step-by-step explanation:

Use the A=Pe^rt equation. A is the end amount, so it's 1892. P is the original amount, 1700. E is a constant, around 2.72. R is the growth constant. T is the time that passed, 3 hours. You can substitute the givens into the equation and get 1892=1700e^(3r). Divide by 1700 to isolate the e. This leaves you with 1892/1700=e^(3r). Do the natural log of each side cancel the e and bring the exponent down. This leaves you with ln(1892/1700)=3r. Divide by 3 to isolate r. ln(1892/1700) is .1. .1/3 is .03333. Multiply by 100 to get a percent. 3.33 percent is your final answer.

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the area of a circle is 60 π sq.cm. find the radius of the radius of the circle to the nearest tenth step-by-step
Svetradugi [14.3K]

Answer:

r = 7.7

Step-by-step explanation:

A = πr²

60π = πr²

r² = 60π/π

r² = 60

\sqrt{r^2} =\sqrt{60}

r = 7.746

Rounded to tenths:

7.7

6 0
3 years ago
Jose wants to find how many gallons of water he needs to fill his cube shaped aquarium. one side of his aquarium is 4 feet long.
MatroZZZ [7]

Answer:

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2 years ago
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Answer:

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Step-by-step explanation:

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2 years ago
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

4^n+17 is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so 4^k+17 is divisible by 3

and we check what happens for k+1

4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17

3\cdot 4^k is divisible by 3 and

4^k+17 is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that 4^n+17 is divisible by 3 for all positive integers n.

Thanks

4 0
3 years ago
Frankie buys six and twelve fifteenths pounds of cherries and four and four sixths pounds of grapes. How many pounds of fruit di
Bas_tet [7]

Answer: I think it’s the 3rd one

Step-by-step explanation:

7 0
3 years ago
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