Final answer:
To rewrite the exponential equation into the desired form, the equation 'y = e^{-0.75t}' is transformed using exponent rules to 'y = (1/e^{0.75})^t', then it is recognized that the constant 'e^{0.75}' can be factored into the form 'y = a(1-r)^t' with 'a=1' and 'r=1 - (1/e^{0.75})'.
Step-by-step explanation:
To rewrite the equation y = e^{-0.75t} in the form of a(1-r)^t, we need to utilize the properties of exponents.
Since e is the base of the natural logarithms, and using the property that e^{-x} = (1/e)^x, the equation can initially be rewritten as:
y = (1/e^{0.75})^t
Next, recognize that e^{0.75} is a constant and can be rewritten as 1/(e^{0.75}) which is essentially a rate r.
If we define a = 1, the final equation can be framed as:
y = a(1-r)^t
where a equals 1 and r equals 1 - (1/e^{0.75}).