More Algebra 2

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It would be great if, again, someone would check these answers for accuracy. I'd like to know if I'm doing them right.

1) What equation defines an exponential decay function?
a) y=x^pi
b) y=pi^-x
c) y=(1/pi)^-x
d) y=pi times x

I think the answer is c.

2) Suppose a lake is clouded with sediment so that the intensity I of the light that passes through the water is reduced by 10% for each 15 cm. of depth. An equation that models this situation is I = (.9)^d/15, where I is the fraction of light that can pass through and d is the depth in cm. At what depth would only 3% light pass through water?
d=500 cm

3) Solve 3 x 5^t = 3/25.

4) Solve ln x = -1.1.

5) Solve 7^r-3 = 200.
r=5.73 (This one I really am not sure about)

6) Project managers in the U.S. space program have determined that an individual's reaction time R can be calculated by the formula R=0.17 + 0.44 log N, where N is the # of choices presented to the individual. Use the formula to determine how many choices would result in a reaction time of .56 seconds. Round your answer to the nearest whole #.
N=about 6 choices

1) less than one taken to a negative power is greater than one taken to a positive power.

4. I don't get that exact answer. x= antiln -1.1

1) So...I'm still confused. Would the answer then be a? or d?

4) How do I go about doing x=antiln?

Are all of the rest of them okay?

for #1 it is b)
As x gets larger, pi^-x gets smaller.

in c) (1/pi)^-x is the same as pi^x, so it would be increasing.

your answers for #2,3, 4,and 5 are correct.
for #5, here is how I would do it:
7^(r-3) = 200
r-3 = ln 200/ln 7 , from a^x = b ---> x = ln b/ ln a
r-3 = 2.7228
r = 5.7228

for #6

.56 = .17 + .44log N
.39 = .44 log N
.8863636 = log N
N = appr. 7.7

Thank you SO much! I get it now. :)

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