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Use the properties of exponents to rewrite y=e^-0.75t in the form of a(1-r)^t

User Jmdeldin
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2 Answers

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20 votes

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}).

User David Narayan
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18 votes
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Answer: y = (1 - 0.527)^t

Step-by-step explanation:

y=e^(-0.75t)


y=(e^-0.75)^t


y= 0.47236655^t


1 - 0.47236655 = 0.52763345

y = (1 - 0.527)^t

User Bernd Verst
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