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Bas_tet [7]
3 years ago
13

The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)4t. There are 50 bacteria prese

nt initially and a biologist wishes to find out how many hours will elapse until there are 10,000 bacteria present. What is the exact value for the number of hours elapsed, t, in the equation 10,000 = 50(10)4t?
Mathematics
1 answer:
andreyandreev [35.5K]3 years ago
8 0

Answer:

t = (log200)/4 hours

Step-by-step explanation:

10,000 = 50(10)^(4t)

Divide both sides by 50

200 = 10^(4t)

Take the log of both sides

log200 = 4t

Divide both sides by 4

(log200)/4 = t

t = (log200)/4    (exact answer)

t ≈ 0.575257498915995 (numeric approximation)

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Alaina wants to decide whether her current cell phone plan is better than a package that another company offers. To compare the
laiz [17]

Hello, this is a linear problem so we are working with y = mx + b

The problem tells us:

y = total cost

x = the megabytes of data that she used in a month

b = y-intercept, which is the initial value

The problem asks "Which part of the graph will represent the cost per megabyte of data used in each plan?"

It is asking for cost per megabyte... This is a rate. and m = slope = rate

So lets, reiterate.

y = total cost

x = the megabytes of data that she used in a month

b = y-intercept, which is the initial value

m = slope = rate = cost per megabyte of data used

Answer: The slopes of the two lines.

6 0
3 years ago
---- PLEASE HELP <3 .. with steps :( <3
Zielflug [23.3K]

1) 6, 18, 54

2) 5/3, 14/9, 41/27

3) 1.5, 2.5, 2.5

Step-by-step explanation:

1)

The function that we have in this problem is

g(x)=3x

We want to find the first 3 iterations.

The initial value is:

x = 2

To find the value of the 1st iteration, we just substitute this value into the expression of the function, and we get:

g_1(x)=3x=3\cdot 2 = 6

The to find the value of the 2nd iteration, we just substitute this value into the expression of the function, and we get:

g_2(x)=3\cdot g_1(x)=3\cdot 6 = 18

Finally, the 3rd iteraction is given by:

g_3(x)=3g_2(x)=3\cdot 18=54

2)

Here in this problem the function that we have to use is

g(x)=\frac{1}{3}x+1

The initial value is

x=2

So the first iteration is given by

g_1(x)=\frac{1}{3}\cdot 2 + 1 = \frac{5}{3}

To find the 2nd iteration, we substitute this value into g(x) again:

g_2(x)=\frac{1}{3}g_1+1=\frac{1}{3}\cdot \frac{5}{3}+1=\frac{5}{9}+1=\frac{14}{9}

Finally, to find the 3rd iteration, we substitute this value into g(x) again:

g_3(x)=\frac{1}{3}\cdot \frac{14}{9}+1=\frac{14}{27}+1=\frac{41}{27}

3)

The function in this problem is

g(x)=-|x-2|+3

The initial value is

x = 0.5

So, the first iteration is:

g_1(x)=-1|0.5-2|+3=-1|-1.5|+3=-1\cdot 1.5 +3=-1.5+3=1.5

The second iteration is given by

g_2(x)=-|g_1-2|+3=-|1.5-2|+3=--0.5+3=2.5

Finally, the 3rd iteration is

g_3(x)=-|g_2-2|+3=-|2.5-2|+3=-0.5+3=2.5

5 0
3 years ago
What is the completely factored form of f(x)=x3+5x2+4x−6?
Gre4nikov [31]
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
3 0
3 years ago
2) If it is 12° outside and the temperature is going to -7° drop 19º. What will the new temperature be? ​
shutvik [7]

Answer:

69 degrees

Step-by-step explanation:

yeah

3 0
2 years ago
Jason eats 10 ounces of candy in 5 days how long does it take Jason to eat one pound of candy
tester [92]

there are 16 ounces to a pound

10/5 = 2 ounces per day

16/2 = 8

 so it took 8 days to eat 1 ppound

6 0
3 years ago
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