Sangeetha Pulapaka

The function which is equivalent to A(t) is function 4, which is, A(t) = 5000(1.013)^{t}(1.013)^{25}

The given function is A(t) = 5000(1.013)^{t+25}

Recall the exponent formula x^{m}\cdot x^{n} = x^{m+n}

Since the base is equal the powers can be added and vice versa.

or x^{m+n} = x^{m}\cdot x^{n}

Replace x with 1.013, m with t and n with 25, then  (1.013)^{t+25} = (1.013)^{t}(1.013)^{25}

So, A(t) = 5000 (1.013)^{t}(1.013)^{25}  

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