Write a function rule that gives the total cost c(p) of p pounds of sugar if each pound costs $0.59. A. c(p) = 59p B. c(p) = C.
2 answers:
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Answer:
Step-by-step explanation:
The compound interest formula is equal to
where
A is the Final Investment Value (future value)
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
To be clear, the given relation between
time and female population is an integral:<span>
</span><span>
</span>
</span>
</span>= <span><span>
In order to evaluate this integral, we need to write this rational function in a simpler way:
</span>
</span>where we need to evaluate A and B. In order to do so, let's calculate the LCD:<span>
</span>
</span>the denominators cancel out and we get:<span>
</span>P + 400 = 0.2AP - 400A + BP<span>
</span> = P(0.2A + B) - 400A<span>
</span>The two sides must be equal to each other, bringing the system:<span>
</span>
</span>Which can be easily solved:<span>
</span>
</span>Therefore, our integral can be written as:<span>
</span>
</span>=
</span>=
</span>= - ln |P| + 6 ln |0.2P - 400| + C<span>
</span>Now, let’s evaluate C by considering that at t = 0 P = 10000:<span>
</span>0 = - ln |10000| + 6 ln |0.2(10000) - <span>400| + C
C = ln |10000</span>| - 6 ln |1600|<span>
</span>C = ln (10⁴) - 6 ln (2⁶·5²)<span>
</span>C = 4 ln (10) - 36 ln (2) - 12 ln (5) <span><span>
</span></span><span><span> </span>Therefore, the equation relating female population with time requested is:<span>
</span><span>t = - ln |P| + 6 ln |0.2P - 400| + 4 ln (10) - 36 ln </span>(2) - 12 ln (5)</span></span>