Modelling with exponential fuction.

The growth rate of a plant during the first week after germination is given by g(t)=ae^(t/2) mm/day, where the time t is measured in days, and a is a constant.

a) Determine the height of the plant h(t) as a function of the time t, assuming that it was zero at time t=0.

b)On the first day, the plant grew 1 mm. Determine the constant a.

c) How much did the plant grow on the fifth day (i.e. between t=4 and t=5)?

I don't know if I'm doing this right. I got h(t)=a(2e^t/2 - 2) for part a and a=1 for part b. Is that right?