Which Logarithmic Graph Can Be Used to Approximate the Value of Y in the Equation 4y = 5?
function a
answer: a reasonable domain is where n is a real number. so n can be between 0 and 10. both endpoints are included.
work shown:
n is the number of days afterwards the experiment starts. the smallest n tin can be is n = 0 which ways that 0 days take gone by, and we're at the start. to observe out how large due north should be, then replace f(n) with xvi.13 and solve for n. use logarithms to isolate the exponent.
f(n) = 12*(1.03)^n
sixteen.13 = 12*(1.03)^n
xvi.thirteen/12 = (one.03)^northward
1.34416666666667 = (1.03)^n
(1.03)^north = 1.34416666666667
log[ (1.03)^n ] = log[ 1.34416666666667 ]
n*log[ ane.03 ] = log[ 1.34416666666667 ]
due north = log[ i.34416666666667 ]/log[ 1.03 ]
north = 10.0062999823929
this rounds to north = 10 which is fairly close merely non 100% perfect. and so this is the largest n can be.
note: if you plug n = 10 into f(n), you'll become roughly 16.127 which rounds to 16.13 (this comes up again in part c)
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function b
respond: the y intercept is 12. it represents the starting height of the plant in cm.
work shown:
plug n = 0 into the f(n) part. simplify
f(n) = 12*(one.03)^n
f(0) = 12*(i.03)^0
f(0) = 12*(1)
f(0) = 12
on day n = 0, aka the starting point, the height f(n) is 12 cm
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part c
reply: the average rate of change is approximately 0.43061036458991 (circular however y'all demand to). this represents the average growth rate from solar day n = three to solar day due north = ten. so the establish grew roughly 0.43 cm per solar day during this timespan, assuming you round to 2 decimal places.
work shown:
compute f(iii)
f(n) = 12*(one.03)^n
f(3) = 12*(1.03)^3
f(3) = thirteen.112724 < nosotros'll use this subsequently
compute f(10)
f(n) = 12*(one.03)^n
f(10) = 12*(1.03)^10
f(10) = 16.1269965521294 < we'll apply this subsequently
now employ the formula below with a = 3 and b = x
aroc = average rate of modify
aroc = [ f(b) - f(a) ]/[ b - a ]
aroc = [ f(10) - f(three) ]/[ x - iii ]
aroc = (sixteen.1269965521294 - 13.112724)/(x - 3)
aroc = 3.0142725521294/7
aroc = 0.43061036458991
round this nonetheless you need to
note: the establish grew approximately 3.01 cm over seven days, so roughly 0.43 cm per day is the boilerplate growth rate (if yous were to round to 2 decimal places).
Source: https://edusmarthelper.com/mathematics/question9401655
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