I am having trouble with this function can someone assistme? Five years ago the

Question

I am having trouble with this function can someone assistme? Five years ago the population was at 1400 and today only 1000of the birds are alive. Once the population drops below 100,the situation will be irreversible. When will thishappen?

Explanation / Answer

A = population after t years A0= Initial population = 1400 k = rate of decay t = time in years First, you must solve for k. A = A0ekt             Divide by A0 A/A0 =ekt             Now you must take the natural log of each side, due to the propertythat ln(ex) = x ln(A/A0) =kt          Divide byt ln(A/A0)/t =k         Plug in initialvalues for A, A0 and t ln(1000/1400)/5 = k ---> ln(5/7)/5 = k ˜ -.067294 Now take this k (I prefer to use the non-decimal formsince it will be more precise) value and plug it into the originalequation, this time we will be solving for t. OurA0 value stays the same, the A valueis now 100. This process is similar to the process we usedabove to solve for k. A = A0ekt A/A0 = ekt ln(A/A0) = kt ln(A/A0)/k = t      We have nowsolved for t, now just plug in the values for ourvariables. ln(100/1400) / (ln(5/7)/5) = t ˜ 39.22 years Hope this helps and be sure to check my work!

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