Really need help finding the exponential model A certain tow

Really need help finding the exponential model!

A certain town is experiencing a population boom. In 1990, the population was 870 and five years later it was 1210. Find a linear model/(x) for the population of the town in the year 1990 + x./(x) = 870 + 68x Find an exponential model p(x) for the population of the town in the year 1990 + x. (Round values to three decimal places.) What do these models estimate the population of the town to be in the year 2000? (Round your answers to the nearest whole number.)/(2000) = people p(2000) = people

Solution

a) 1990 ----pop. 870

five years later : 1995 ---pop. 1210

slope = ( 1210- 870/(5) = 340/5 = 69

So, l(x) = 870 +68x

b) l(x) = loe^kx

lo = 870

x =5 l(x) = 1210 . find k

1210 = 870e^(5k)

0.329 = e^5k

0.329 = 5k----> k = 0.0659

p(x) = 870e^(0.0659x)

b) x = 10 ; l(10) = 870 +69*10 = 1560

p(10) = 870e^(0.0659*10) = 870*1.932 = 1682