Try solving for the variable and get everything to one side
F(x)=10-16/x
f'(x)=16/x^2
f'(c)=16/c^2
f(8)=10-16/8=10-2=8
f(2)=10-16/2=10-8=2
![f'(c)= \frac{f(b)-f(a)}{b-a} in (2,8), \frac{16}{c^2} = \frac{f(8)-f(2)}{8-2} , \frac{16}{c^2} = \frac{8-2}{8-2} ](https://tex.z-dn.net/?f=f%27%28c%29%3D%20%5Cfrac%7Bf%28b%29-f%28a%29%7D%7Bb-a%7D%20in%20%282%2C8%29%2C%0A%20%5Cfrac%7B16%7D%7Bc%5E2%7D%20%3D%20%5Cfrac%7Bf%288%29-f%282%29%7D%7B8-2%7D%20%2C%0A%20%5Cfrac%7B16%7D%7Bc%5E2%7D%20%3D%20%5Cfrac%7B8-2%7D%7B8-2%7D%0A)
4∈[2,8] is the required point.
Step-by-step explanation:
So the general formula for compound interest is
where t is typically time in years, and n is how many times it's compounded per year. But in this case it's only compounded 1 time per year so the equation is just
. in this case P is the principal amount, r is the interest, and A is the final amount. So the 5% interest rate becomes 0.05 by dividing by 100 to convert it into decimal form and the principle amount of 11,000. This gives you the formula
. This is the answer to the first question where t is the time in years. When it says "Find interest earned" I'm a bit confused, is it giving you x amount of years where you have to calculate the interest earned or does it want a general equation? Because the general equation would be the final amount - the principle amount which calculates the difference. So the equation for interest earned would be
. To calculate the amount of money after 5 years you simply plug in 5 as t. this gives you the equation ![11000(1.05)^5 \approx 11000(1.276) \approx 14,039.10](https://tex.z-dn.net/?f=11000%281.05%29%5E5%20%5Capprox%2011000%281.276%29%20%5Capprox%2014%2C039.10)
f = 2
Simplify both sides of the equation <span><span>1.25f</span>+2</span>=<span><span>−<span>2.75f</span></span>+<span>10
Add 2.75 to each side </span></span><span><span>4f</span>+2</span>=<span>10
Subtract 2 from both sides </span><span>4f</span>=<span>8
Divide each side by 4 </span>f=<span>2</span>
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