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Every year, a marine biologist measures the sea turtle population in Sunny Harbor. When he first measured the population one year ago, there were 640 sea turtles. Now, the sea turtle population has increased to 800. The biologist expects the population to continue increasing each year.
Write an exponential equation in the form y=a(b)x that can model the sea turtle population, y, x years after the initial measurement.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =

How many years after the marine biologist first measured the population does he expect it will reach 1,250?
years



Answer :

Answer:

Step-by-step explanation:

y = yo  b^x    in year 0   y = yo = 640

640 = 640  b^0     then in year 1   y = 800 and yo = 800

800 = 640 b^1    shows b =   800/640 = 1.25

so your equation becomes

y = 640 (1.25)^x      where 'y' is the population in 'x' years

find when population = 1250 :

  1250 = 640 (1.25)^x

   1250 / 640 = 1.25^x

         log (1250/640) =  x log 1.25

             x =   log (1250/640) / log(1.25) = 3 years

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