A segmental organism grows by adding new segments at intervals of 24 hours. Suppose that initially (call it day 0) there is only one terminal segment and that in the following day (call it day 1) there are two terminal segments (see Figure 1). From there on new segments grow according to the following model: a_n+1 - beta a_n - gamma a_n-1 = 0 where a_n is the number of terminal segments at day n and beta and gamma are constants. a. what is the biological meaning of beta and gamma? b. Write this equation as a system of two first order equations. c. For beta = 2 and gamma = 1: i. Find a general solution for the system you wrote in Question 1b and sketch a few typical solutions on a phase portrait. ii. Find an analytical solution for a_n that satisfies the initial condition shown in Figure 1. iii. Write a computer program to calculate a_n and compare your results with the analytical solution. iv. Determine how many terminal segments there will be on day 3 and sketch the A segmental organism grows by adding new segments at intervals of 24 hours. Suppose that initially (call it day 0) there is only one terminal segment and that in the following day (call it day 1) there are two terminal segments (see Figure 1). From there on new segments grow according to the following model: a_n+1 - beta a_n - gamma a_n-1 = 0 where a_n is the number of terminal segments at day n and beta and gamma are constants. a. what is the biological meaning of beta and gamma? b. Write this equation as a system of two first order equations. c. For beta = 2 and gamma = 1: i. Find a general solution for the system you wrote in Question 1b and sketch a few typical solutions on a phase portrait. ii. Find an analytical solution for a_n that satisfies the initial condition shown in Figure 1. iii. Write a computer program to calculate a_n and compare your results with the analytical solution. iv. Determine how many terminal segments there will be on day 3 and sketch the