can someone solve this problem? with step by step

Question

The formula A=134e^0.032t models the population of a particular city , in thousands, t years after 1998. When will the population of the city reach 168 thousand?

Answer 1

134e^0.032t = 168

 

     e^0.032t = 1.2537313

 

      0.032t = ln(1.2537313)

 

             t = 7.066 years after 1998

 

 

Answer 2

Set A=168 and solve for t.  Since t is an exponent and we have the number e, we natural log both sides of the equation.

 

ln(168000) = ln(134e^0.032t)

 

 

Bring the exponent down as the coefficient of ln.

 

ln(168000) = 0.032tln(134e)

 

ln(168000) = 0.032[ln(134) + ln(e)]

 

ln(168000) = 0.032tln(134) + 0.032ln(e)

 

ln(168000) = 0.032tln(134) + 0.032

 

12.0317 = 0.032t(4.8978) + 0.032

 

 

Apply simple algebra to solve for t.

 

Once you have solved for t, round it to the nearest integer and add 1998 to it to get the actual year.