Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation

a(t) = 210 - 5t

(1) What does t represent?

Since t is given in minutes, it stands for time.

Interpreting t as the balloon’s altitude is incorrect since a(t) represents altitude.

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Time elapsed since the balloon starts descending

This is the correct interpretation.

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Time for the balloon to reach ground level is incorrect because that would be a fixed moment, not a variable t.

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(2) What does a(t) represent?

The balloon’s altitude

This is the correct answer.

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Time since descent began is incorrect because that is represented by t.

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Time to reach the ground is inaccurate since a(t) is altitude, not time.

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(3) What does a(5.5) signify?

It does not represent the time to reach 5.5 feet altitude.

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The altitude of the balloon after 5.5 minutes

This is the correct interpretation since a(5.5) is altitude when t = 5.5 minutes.

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It is not the time needed to reach the ground.

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5.5 minutes alone is not correct because a(t) denotes altitude, not time.

a(5.5) refers to altitude at t = 5.5 minutes.

Answer:

Please refer to the explanation

Step-by-step explanation:

Given that:

Sarah, Jose, and you all reside on the same street:

The distance between you and Jose is 5 blocks

The distance between Jose and Sarah is 2 blocks

Calculating the distance (b) between you and Sarah:

Since it is not specified if Sarah is closer to you or to Jose;

Thus;

Distance b from you to Sarah will be:

(The distance to Jose ± the distance to Sarah)

b = (5 ± 2)

b = (5 + 2) or (5 - 2)

b = 7 blocks or 3 blocks

11,000 multiplied by 16% equals $1,750, which when multiplied by 4 gives a total of $7,040.

Therefore, after 4 years, the car's value is $11,000 - 7,040 = $3,960.

Answer:

The universal formula applicable for determining the necessary combinations of n ice cream flavors.

For 10 flavors of ice cream

Step-by-step explanation:

Let's denote V = Vanilla, C = Chocolate, S = Strawberry, P = Pineapple, B = Berry

For 2 flavors of ice cream:

V, C

{V/V, V/C, C/C}

3 possible combinations

For 3 flavors of ice cream:

V, C, S

{V/V, V/C, V/S, C/S, C/C, S/S}

6 possible combinations

For 4 flavors of ice cream:

V, C, S, P

{V/V, V/C, V/S, V/P, C/S, C/P, S/P, C/C, S/S, P/P}

10 possible combinations

For 5 flavors of ice cream:

V, C, S, P, B

{V/V, V/C, V/S, V/P, V/B, C/S, C/P, C/B, S/P, S/B, P/B, C/C, S/S, P/P, B/B }

15 possible combinations

Thus, we derive a sequence of

3, 6, 10, 15...

This sequence is recognized as the Triangular number series

1 + 2 = 3

1 + 2 + 3 = 6

1 + 2 + 3 + 4 = 10

1 + 2 + 3 + 4 + 5 = 15

The general formula for this sequence is

Utilizing this formula allows us to predict the number of 2-scoop combinations from 10 flavors.

Consequently, there are 55 varying combinations for a 2-scoop cone when selecting from 10 flavors.

You might consider utilizing the following dataset:
0 0
1 60
2 120
3 180
4 240
5 300
6 360
7 420
8 480
9 540
10 600
This information illustrates a function of:
y = 60x
This indicates that the vehicle achieves 60 miles per gallon.
The distance covered per gallon exceeds that of Mr. Miller's vehicle.