Growth rate

Historically, the rate of growth of output over time has exceeded the growth rate that can be attributed to the growth in conventionally defined inputs like labour and capital.
If q=A(t) f(k,l) (equation 1) is the society’s output as a whole

The term A(t) in the function represents all the influences that go into determining q other than k (machine hrs) and l (labour hrs). Changes in A overtime represent technical progress, such that A is a function of time. That is dA/dt>0 and particular levels of inputs of labour and capital become more productive over time. Since for any variable X, dx/dt/x is the proportional rate of growth per unit of time;
i) Write the equation 1 above in terms of growth rates
ii) Find the elasticity of output with respect to capital input and labour input.
iii) Derive and show the component of growth that can be attributed to technical progress.