Consider an organism growing according to S(t) = S(0)et. Suppose = 0.001/s, and S(0) = 1.0

Consider an organism growing according to S(t) = S(0)eαt. Suppose α = 0.001/s, and S(0) = 1.0 mm. At time 1000 s, S(t) = 2.71828 mm. How close must t be to 1000 s to guarantee a size within 0.1 mm of 2.71828 mm?
Find the accuracy of input necessary to achieve the desired output accuracy.