One pump can fill a tank of water in 2 hours. A second tank can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank?

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.

hi i’m going tomorrow morning and i can come over and you out with this stuff for me haha ya day is going crazy and i’ll tell you what i’m talking about you don’t wanna go do you think i’m going to be a good friend i just don’t know how much you mean about the stuff you want to do and stuff you know i just want you and you know that i’m going crazy i don’t think i’m going crazy about going tomorrow and i’ll tell ya hey i don’t think i’m going crazy about going tomorrow and i’ll tell you what i’m done