SOLUTION: how to find the y=ab^x equation for a graph that passes through the points (2,45) and (5,1215)

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Question 947531: how to find the y=ab^x equation for a graph that passes through the points (2,45) and (5,1215)
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Choose the base you want. Base ten is used here.

log%2810%2Cy%29=log%2810%2C%28ab%5Ex%29%29
log%2810%2Cy%29=log%2810%2Ca%29%2Bx%2Alog%2810%2Cb%29
highlight%28log%2810%2Cy%29=x%2Alog%2810%2Cb%29%2Blog%2810%2Ca%29%29
This equation is now in linear form.

The given points need to be reprocessed to fit with the linear formed equation. The vertical axis coordinates must be log%2810%2C45%29 and log%2810%2C1215%29.

The slope of the line is highlight_green%28log%2810%2Cb%29=%28log%2810%2C1215%29-log%2810%2C45%29%29%2F%285-2%29%29.
Solve for b.

Slope-intercept form will still be convenient to use for find the vertical axis INTERCEPT. Recall f=mx%2Bv;
If v is for vertical axis intercept, f for the vertical axis value at any x,
v=f-mx.
Choose either of your treated points which fit the linearized equation, the now found slope, and solve for the value of your vertical axis intercept.