Question

How do you write an exponential equation that passes through (-1, .5) and (2, 10)?

Answer 1

I found: `color(red)(y=0.5e^(1+x)`

Explanation:

In general the equation will be of the form:
`y=ke^(cx)`
where: `k and c` are constants to be found:
let us use our points and substitute into our general equation:
`{(0.5=ke^(-c)),(10=ke^(2c)):}`
from the first:
`k=0.5/e^-c=0.5e^c`
substitute into the second:
`10=0.5e^c*e^(2c)`
use the law of exponents and get:
`e^(c+2c)=10/0.5=20`
take the `ln` on both sides:
`3c=ln(20)`
`c~~1`
substitute back into `k=0.5/e^-c=0.5e^c`:
`k=0.5e`
so finally your equation will be:
`color(red)(y=0.5e*e^x=0.5e^(1+x)`

Graphically: