The population growth of an animal species is described by F(t) = 500 + 90 log(base3) (2t + 1) where t is meas

Question

The population growth of an animal species is described by F(t) = 500 + 90 log(base3) (2t + 1) where t is measured in months. Find the population of this species in an area 40 month(s) after the species is introduced.

Answer 1

F(t) = 500 + 90 logbase3 (2t+1)

we know that "t" represents time in months, and we are asked to find the population in 40 months.  so, we can plug 40 in for "t".

= 500 + 90 logbase3 (2*40 +1)

solve whats in the parenthasis.

= 500 + 90 logbase3 (81)

now we need to temporarily ignore the 500 and solve "90logbase3 (81)"

90 logbase3 (81)

but 1st, we have to solve for "logbase3 (81).  if we set that expression equal to x, then we can change the equation from logarithmic form, to exponential form.

logbase3 (81) = x      turns into    3^x = 81

so, 3 must be multiplied by itself how many times to equal 81?  the answer is 4.

3^4 = 81

so, now that we know logbase3 (81) equals 4, we can subsitute that in our equation.

= 500 + 90 logbase3 (81)  turns into...

= 500 + 90 (4)

now, you can use algebra to solve the rest!

= 500 + 360

= 860

the population is 860.

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