Help with finding exponential model A certain town is experi

Help with finding exponential model?

A certain town is experiencing a population boom. In 1990, the population was 870 and five years later it was 1230. Find a linear model l(x) for the population of the town in the year 1990 + x. 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.)

Solution

the exponential equation isy=a e^(kt)

here a=870

t=5

y=1230

1230=870e^(5k)

1230/870= e^(5k)

taking ln both sides

ln(1230/870)=5k

k=ln(1230/870)/5

k=.069( upto 3 decimal place)

required equation is p(x)= 870e^(.069x)