The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500? F.2084
G.2044
H.2043
J.2085

9514 1404 393

  J. 2085

Step-by-step explanation:

Fill in the desired value for y and solve for x.

  1500 = 50(1.05^x)

  30 = 1.05^x . . . . . . . divide by 50

  log(30) = x·log(1.05) . . . . . take logarithms

  x = log(30)/log(1.05) ≈ 69.71

Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)