Please help me with my Algebra 2 :)

Question

Ok, so I was a bit lost when my teacher explained how to do these problems on a calculator. Please help me learn how to do it on a calculator, or just how to solve these examples! Thanks!

1) Write an exponential function y=ab^x whose graph passes through the given points.

(0, 1), (2, 4)

2) Use the table of values to determine whether or not an exponential model is a good fit for the data (x, y).

x : ln y

1 :2.91

2 :3.55

3 :4.26

4 :5.22

5 :6.29

6 :7.43

3) Find an exponential model by solving for y.

ln y = 1.024x + 1.668

4) Write a power function y = ax^b whose graph passes through the given points.

(1, 3), (2, 24)

5) Use the table of values to determine whether or not a power model is a good fit for the data (x, y).

ln x : ln y

0 :1.233

0.693 :2.198

1.099 :3.125

1.386 :4.302

1.609 :4.630

1.792 :5.741

6) Find a power model by solving for y.

ln y = 3 ln x

Answer 1

I will do the first one

if the graph passes through (0,1) and (2,4) then just substitute these values into the equation

y=ab^x then

1=a(b^0) a=1

if a=1 then 4=1(b^2) so b=2 therefore the equation is y=2^x