the formula A= P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using the base e, A=Pe^kt.

Can someone explain the answer in detail? I know the final answer, but I don't understand the process of getting there

Question

the formula A= P(1.09)^t is an example of exponential growth with base 1.09. Determine an equivalent continuous growth formula using the base e, A=Pe^kt.

Can someone explain the answer in detail? I know the final answer, but I don't understand the process of getting there

anonymous · Answer

dy/dt = 0.09 y  9% growth per time period dt

dy/y =  0.09 dt

ln(y) = 0.09 t

A = P  exp(0.09 t)      continuous compounding rather than yearly
 compare at t=1 year

A/P = 1.09 vs

 A/P = exp(0.09) = 1.094

anonymous · Answer

I don't understand? the answer is A= Pe^0.086t?