Rewrite y=3e^-0.6 in the form of y=a(1+r)^t or y=a(1-r)^t. Round to the nearest ten thousandths

Answer 1

We want to rewrite the exponential function;

y = 3e^{-0.6t \}

in the form:

y = a (1 + r) ^t or y = a (1 − r) ^t

Step 1: The constant in front stays the same:

a = 3

Step 2: Rewrite e^-0.6

e ^-0.6 ≈ 0.5488

So, the function becomes:

y = 3 (0.5488)

Step 3: Convert to 1 - r form

Since 0.5488 < 1, it represents decay:

0.5488 = 1 - r

r = 1 - 0.5488

r = 0.4512

Final Answer (rounded to nearest ten-thousandth):

y = 3 (1 - 0.4512)

Note: If your problem actually intended the standard exponential model y = 3e^-0.6t, then the correct rewritten form would be:

y = 3 (1 - 0.4512) ^t