C: none of these are solutions to the given equation.
• If<em> y(x)</em> = <em>e</em>², then <em>y</em> is constant and <em>y'</em> = 0. Then <em>y'</em> - <em>y</em> = -<em>e</em>² ≠ 0.
• If <em>y(x)</em> = <em>x</em>, then <em>y'</em> = 1, but <em>y'</em> - <em>y</em> = 1 - <em>x</em> ≠ 0.
The actual solution is easy to find, since this equation is separable.
<em>y'</em> - <em>y</em> = 0
d<em>y</em>/d<em>x</em> = <em>y</em>
d<em>y</em>/<em>y</em> = d<em>x</em>
∫ d<em>y</em>/<em>y</em> = ∫ d<em>x</em>
ln|<em>y</em>| = <em>x</em> + <em>C</em>
<em>y</em> = exp(<em>x</em> + <em>C </em>)
<em>y</em> = <em>C</em> exp(<em>x</em>) = <em>C</em> <em>eˣ</em>
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Answer:
there are 184 cats and dogs in the world.
We want to see how much the population of goats grows each year. We will see that the correct option is c: 17%.
<h3>
Exponential growth of populations</h3>
We know that:
- The initial number of goats is 1,500.
- After 11 years, the population is 8,400.
The population can be modeled with an exponential equation as:
P(t) = A*(1 + r)^t
Where:
- A is the initial population.
- r is what we want to find, it depends on how much the population increases.
- t is the time in years.
So we have:
P(t) = 1500*(1 + r)^t
And we know that after 11 years the population is 8,400, so we have:
P(11) = 1500*(1 + r)^11 = 8400
Now we can solve this for r:
(1 + r)^11 = 8400/1500 = 5.6
(1 + r) = (5.6)^(1/11) = 1.17
r = 1.17 - 1 = 0.17
r = 0.17
To get it in percentage form, you just need to multiply it by 100%
0.17*100% = 17%
This means that the population increases a 17% each year, so the correct option is c.
If you want to learn more about exponential growth, you can read:
brainly.com/question/13223520
