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lukranit [14]
3 years ago
12

Caswell started studying how the number of branches on his tree grows over time. The relationship between the elapsed time ttt,

in years, since Caswell started studying the tree, and the number of its branches, N(t)N(t)N, left parenthesis, t, right parenthesis, is modeled by the following function: N(t)=15⋅(1.64)t3.4 Complete the following sentence about the rate of change in the number of branches.
Mathematics
2 answers:
ipn [44]3 years ago
8 0

Answer:

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

Step-by-step explanation:

100 = 5 * 10^(0.3t), solve for t

Divide both sides by 5:

20 =10^(0.3t)

Take the log of both sides:

0.3t =log(20)

Divide both sides by 0.3:

Multiply the RHS by 10 / 10

t =log(20) / 0.3 = 10*log(20) / log(1,000) - years - when the tree will have 100 branches.

Sidana [21]3 years ago
4 0

Answer:

Step-by-step explanation:

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If randy earns $12.74 per hour, what is his overtime rate? How much should randy make if he works 45 1/2 hours during 1 week?
elena-14-01-66 [18.8K]

Answer:

$19.24 is the overtime rate $579.67 one week

Step-by-step explanation:

So $13.00 its $19.50 so I subtracted $12.74 to $13.00 got 0.26 then subtracted $19.50 by 0.26 and got $19.24

$12.74 times 45.5 that will be $579.67 for just one week

If I didn't get it right. Tell me in the comments. I think I got it right.

8 0
3 years ago
Can someone tell me if these answers are right or not? These problems are getting on my nerves!
Bond [772]
1a. 3^1 / 3^2 = 3^1-2 = 3^-1 = 1/3^1 = 1/3.
2b. 4^2 / 4^4 = 4^2-4 = 4^-2 = 1/4^2.
3c. 6^3/6^5 = 6^3-5 = 6^-2 = 1/6^2.
4d. 3^-5 • 3^2 = 3^-10 = 1/3^10.

I believe for the last question its asking only to rewrite exponent as a positive exponent similar to the first question.
6 0
3 years ago
Mary wants to make 20 gallons of a 52% acid solution by mixing together a 84% acid solution and a 4% acid solution. How much of
Setler [38]

Answer:

  • 12 gallons 84%
  • 8 gallons 4%

Step-by-step explanation:

I like to use an "X-diagram" to solve mixture problems. On the left side are the constituents of the mix; in the middle is the result of the mix; and on the right side are the differences between the numbers on each diagonal. These differences are the ratio numbers for the mix.

Here, that means the ratio of 84% solution to 4% solution is ...

  48 : 32 = 12 : 8

Note that the last two "ratio numbers" were chosen so their sum is 20, hence they represent the number of gallons of the corresponding constituent in the mix. (The sum of the first two ratio numbers is 48+32=80, so to get a sum of 20, we divide each by 4.)

Mary must use ...

  • 12 gallons of 84% acid solution
  • 8 gallons of 4% acid solution

You may note that this solution takes much longer to explain than to do. The math here can all be done without a calculator.

_____

<em>Check</em>

12 × 84% + 8 × 4% = 10.40 = 20 × 52%

_____

<em>Usual Solution</em>

A more conventional approach would be to assign x to the amount of 84% solution needed. Then the number of gallons of acid in the mix is ...

  0.84x + 0.04(20 -x) = 0.52(20)

  0.80x + 0.8 = 10.4 . . . . simplify

  0.80x = 9.6 . . . . . . . . . . subtract 0.8; next, divide by 0.8

  x = 9.6/0.8 = 12 . . . . gallons of 84% acid

  20-x = 8 . . . . . . . . . . gallons of 4% acid

3 0
3 years ago
What percent of the bill will you pay if you pay your bill plus a 9.5% tax?
Gelneren [198K]

Answer:

109.5% of the bill

Step-by-step explanation:

You have to pay 100% of your bill (or else you wouldn't have paid your bill in full) and as you said, "plus a 9.5% tax". 100+9.5=109.5%

7 0
3 years ago
What’s a mean,median,and mode?
tamaranim1 [39]

The mean is the average you're used to, where you add up all the numbers and then divide by the number of numbers. The median is the middle value in the list of numbers. Mode is the number which appears most often in a set of numbers.

Hope this helps you :)

5 0
3 years ago
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