SOLUTION: an exponential curve relating two quantities v and t has the form v=ae^kt where a and k are constants. The curve passes through two points (0.2,4.42) and (-2, 1.4715). Determine

Algebra ->  Graphs -> SOLUTION: an exponential curve relating two quantities v and t has the form v=ae^kt where a and k are constants. The curve passes through two points (0.2,4.42) and (-2, 1.4715). Determine       Log On


   

Question 872931: an exponential curve relating two quantities v and t has the form v=ae^kt where a and k are constants.
The curve passes through two points (0.2,4.42) and (-2, 1.4715).
Determine the values of a and k, and find the value of t to 5dp when v=1.5
Any help would be hugely appreciated!
Thanks in advance.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This solution is not the complete answer but only guidance.
The exponential equation is really v=ae%5E%28kt%29.
ln%28v%29=ln%28a%29%2Bkt%2A1
ln%28v%29=ln%28a%29%2Bkt
highlight_green%28ln%28v%29=kt%2Bln%28a%29%29----this is a slope-intercept linear equation.

Using the linearized form of the relationship, change your two given points into (t, ln(v)). The slope, calculable using the formula for slope, will be the value for k. The vertical axis intercept will be ln(a).