Suppose that the per capita growth rate of a population is 2% and at time t=2 the population is equal to 50

Suppose that the per capita growth rate of a population is 2% and at time t=2 the population is equal to 50.

a) Use linear approximation to compute the approximate population size at t=2.1
b) Find the exact size of the population at t=2.1?

I can do part a):

The linear equation for N(t) is:
N(t) = b + (1.02*t) where b is the initial population, 1.02 is the original population (1) plus the amount it changes (20% or .02), and t is time. We know that N(2) is 50, so:
50 = b + (1.02*2)
50 - 2.04 = b
b = 47.96

Now we plug in 47.96 for b to get
N(t) = 47.96 + (1.02*t)
at t = 2.1, we can solve for N(2.1):
N(2.1) = 47.96 + (1.02*2.1)
N(2.1) = 50.102

I'm stuck on part b). I believe you have to use the equation N(t) = b*e^(r*t), where r is the rate of change (20% or .02). However, when I solve the equation and enter it into LON-CAPA (I'm assuming you got this equation from the LON-CAPA calc. homework?) it tells me it's incorrect. Hopefully you can find someone that knows how to do the second part!