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Vladimir [108]
2 years ago
5

A certain population of mice is growing exponentially. After one month there are 48. After 2 months there are "192" mice. Write

an equation that represents this scenario(With work)
Mathematics
1 answer:
REY [17]2 years ago
8 0

Answer:

P(t) = 12e^1.3863k

Step-by-step explanation:

The general exponential equation is represented as;

P(t) = P0e^kt

P(t) is the population of the mice after t years

k is the constant

P0 is the initial population of the mice

t is the time in months

If after one month there are 48 population, then;

P(1) = P0e^k(1)

48 = P0e^k ...... 1

Also if after 2 months there are "192" mice, then;

192 = P0e^2k.... 2

Divide equation 2 by 1;

192/48 = P0e^2k/P0e^k

4 = e^2k-k

4 = e^k

Apply ln to both sides

ln4 = lne^k

k = ln4

k = 1.3863

Substitute e^k into equation 1 to get P0

From 1, 48 = P0e^k

48 = 4P0

P0 = 48/4

P0 = 12

Get the required equation by substituting k = 1.3863 and P0 = 12 into equation 1, we have;

P(t) = 12e^1.3863k

This gives the equation representing the scenario

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Given that (-1, a) is the midpoint of the line segment joining (0, -2) and (b, 8) then find the values of a and b
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Step-by-step explanation:


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3 years ago
A and b are positive integers. Find <img src="https://tex.z-dn.net/?f=-2a%2B3b" id="TexFormula1" title="-2a+3b" alt="-2a+3b" ali
lord [1]

A could be 2 while B could be 3, so -2a+3b turns into -4+9, which equals 5.

From what I know you can't really solve a a single equation with two-variables so it's just a matter of trial and error.

Just try plugging in a small number like 2 for a just to try it and you get 8b^2=72.

Divide everything by 8 to isolate b and you get that b^2=9.

Square root everything and you'll find that b=3. This is just one possible combination, I'm sure there are many more but this is obviously the one that was intended to be found.

Now that we know that a=2 and b=3 just plug them into the equation.

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Sorry about having to use this ^ symbol, the equation maker is not working.

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