in an optimal environment, a bacterial population grows exponentially. At noon in the sewage treatment plant, experimenters introduce specially cultured bacteria into a barrel full of rich nutrients. We will assume that the bacteria population in the barrel is modeled by an exponential function.

Let N(t) be the number of bacteria after t days. Then N(t)= Pa^t for some constants P and a. Measurements indicate that N(2)= 5400 and N(6)= 382000.

Write down 2 equations to compute a and P, one when t=2 and the other when t= 6.

Use these equations to compute P and a. Round your values to three sig digits.