<h3>Given</h3>
Future value of an investment at 4.75% compounded weekly is $25,000
<h3>Find</h3>
The present value of the investment, to the nearest dollar
<h3>Solution</h3>
The multiplier is (1 + .0475/52)^(52·5) ≈ 1.2679375, so the amount required is found from
... 1.2679375×present value = 25,000
... present value = 25,000/1.2679375 ≈ 19,717
$19,717 needs to be placed in the account now.
_____
When an annual interest rate r is compounded n times per year, the annual multiplier is (1 +r/n)^n. Here, we have n=52 (weeks per year). The multiplier is applied 5 times (raised to the 5th power) to obtain the result of a 5-year investment.
2^2. 2 and 2. Because 2 and 2
The exponential equation
is equivalent to the log form equation
The base of the log is the same as the base of the exponent. The 8 inside the log argument is the right hand side of the original equation. The goal with logs is to isolate the exponent, so that's why 3 is on its own side
You can use trig here - you want to know the angle opposite from the shortest side, which we'll call "A," and you have the sides that touch the right angle. side A (21 inches) and side B (25 inches) intersect at a right angle, so the side we're missing is the hypotenuse. the angle across from side A is angle "a" - now, since we know which side is the hypotenuse, we can figure out which trig function works here. angle "a" can be found by doing tan(a)=Opposite/Adjacent --> tan(a)=A/B --> tan(a)=21/25 --> a=tan^-1(21/25). a = 40.03 degrees
1/2-1/4
(1/2x2)-1/4
2/4-1/4
2-1
1
1/4