Question

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.
t=-2

4) Solve ln x = -1.1.
x=0.34

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. :)

Answer 1

How do u do number 2 and 3 and 4 with work plz