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kifflom [539]
3 years ago
14

Two days after a biology experiment there was 49 million bacteria present. Four days after the experiment there was 600.25 milli

on bacteria present. Find an exponential equation that models this situation. Shoe your work please!
Mathematics
1 answer:
nataly862011 [7]3 years ago
8 0

Answer:

y=Ae^(1.25t)

Step-by-step explanation:

From the expression  y=Ae^kt

After two days of the experiment, y = 49 million, t=2

After four days of the experiment, y= 600.25 million, t=4

A is the amount of bacteria present at time zero  and t is the time after the experiment (in days)

At t=2 and y =49

 49=Ae^2k…………….. (1)

At t=4 and y = 600.25

600.25=Ae^4k………… (2)

Divide equation (2) by equation (1)

600.25/49=(Ae^4k)/(Ae^2k )

12.25=e^2k

Take natural log of both sides

ln⁡(12.25) =2k

2.505⁡ =2k

k=1.25

The exponential equation that models this situation is y=Ae^(1.25t)

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Answer: The difference between the larger and smaller number is 21.

Step-by-step explanation:

This can be translated to:

"the multiplication between 3 numbers is 1000 and the addition is 39.

If the first number is at the second like the second at the third, find the difference between the smaller and the larger number"

If A is the first number, B the second and C the third we have that:

A*B*C = 1000

A + C + B = 39

A/B = B/C

From the third equation we have that:

A*C = B*B

we can replace it in the first equation and get:

B*(A*C) = 1000

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A + 10 + 4 = 39

A = 39 - 14 = 25

Then the difference between the larger and smaller number is:

A - C = 25 - 4 = 21

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4 years ago
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