A model for exponential growth of a quantity is given by: At= A0e^(kt) where k=(

Question

A model for exponential growth of a quantity is given by:

At= A0e^(kt) where k=(1/t)ln(At/A0)

In these equations, At and A0 are the quantities at time t and time 0, respectively, and k is a constant that is unique to the specific application. Write a user-defined function that uses this model to find the quantity At. This function, should have four input arguements, 3 scalars A0, At1 and t1 as well as a matrix of values t with one output argument At. The function should verify that all input values are scalar values (not matrices) prior to continuing the calculations. I know that I am supposed to solve for k first using the input variables and then I should be able to solve for At but I'm a little lost on this Matlab problem, any help appreciated!

Explanation / Answer

function At=expGrowth(A0,At1,t1,T)

if isscalar(A0) and isscalar(At1) and isscalar(t1) and !isscalar(t)
   k= (1/t)*log(At1/A0)
else
   error('invalid input')

for i=T
   At(end+1)=A0*exp(k*i)
end

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