Calculus help with finding explicit expression

Question

The population P of city A from 2010 is given by the table. Year 2010 2011 2012 2013 Population 100,500 82,300 67,400 55,200 This seems to follow an exponential decay model P(t) = P0e kt, where t represents t years after 2010.

1. Use the data for 2010 and 2011 to find the explicit expression for P(t). (Round k in your answer to 1 decimal place.)

2. Use your function P(t) to predict the population in 2015.

3. According to P(t), at what time does the population decrease by 50%?

4. Use the nearest right-hand value in the table to estimate P ′ (1), and use P ′ (1) to estimate P(1.1) by linear approximation.

Answer 1

Just a start

82300 = 100500e^k, t = 1

0.8189 = e^k

ln 0.8189 = k

Can you take it from here?