I need help with this problem please.

Question

Find the equation for the linear function that passes through the points (3, 6) and (8, 9).

Round all answers to 4 decimal places as needed

Find the equation for the exponential function that passes through the points (3, 6) and (8, 9).

Round all answers to 4 decimal places as needed



Answer 1

Use the 2 point form to solve the first part: (9-6)/(8-3) = (y-6)/(x-3).

Write the exponential as ln y = ln A + kx.

The 2 points will give you 2 simultaneous linear equations in unknowns ln A and K as follows

ln 9 = ln A + 8k

ln 6 = ln A +3k

Subtraction will eliminate ln A and get you k.

Either equation will then get ln A.

To get the exponential form back you need to get A= e^{ln A}.