Provide step by step solution to the following questions.

The mortality rates for a population for the age range 30-34 were estimated by fitting a straight line or + Bx to the crude values of log (q, /p. ). Test whether this model (with estimated parameter values of a =-10.9446 and =0.110404) can be considered to give a good fit to the data shown in the table below for 2003. Age x 30 31 32 33 34 Number of deaths in 2003 335 391 428 436 458 The initial exposed to risk in 2003 was approximately 700,000 at each age.A company is considering investing in the following project. The company has to make an initial investment of three payments, each of $105,000. The first is due at the start of the project, the second six months later, and the third payment is due one year after the start of the project. After 15 years it is assumed that a major refurbishment of the infrastructure will be required, costing $200,000. The project is expected to provide no income in the first year, an income received continuously of f20,000 in the second year, $23,000 in the third year, $26,000 in the fourth year and $29,000 in the fifth year. Thereafter the income is expected to increase by 3% per annum (compound) at the start of each year. The income is expected to cease at the end of the 30th year from the start of the project. The cash flow within each year is assumed to be received at a constant rate. (i) Calculate the net present value of the project at a rate of interest of 8% pa effective. [8] (ii) Show that the discounted payback period does not fall within the first 15 years, assuming an effective rate of interest of 8% pa. [5] (iii) Calculate the discounted payback period for the project, assuming an effective rate of interest of 8% pa. [5] [Total 18]1. [8 points] Let the production function be Q (t) = f (t, K(1). L()) = exp (gt) K(t)" L(t) 1-, (1) where Q is total output, f () is the production function, K is capital input, I is labor input, and f is the time which indicates that the production function can shift over time due to technological changes. The notation exp (.) denotes the exponential function, g > 0 is a constant, and a E (0, 1) is the share of capital in the production function. Derive the expression of the growth rate of Q (f), i.e., Q(t) (2) in terms of the growth rates of capital and labor, and K(!) L(t) and two model parameters, a and g