Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease to the nearest 10th.

Question

Exponential function: y=700(2)^-x/33

Answer 1

Exponential function: y=700(2)^-x/33

We rewrite the base: 2^-x/33 = ((1/2)^1/33)^x = .9792145972^x

Since the base is less than 1, it represents decay. 1 - r = .9792145972 => r = .0207854028

Hence, r = 2.07854... ~ 2.1%. percent rate of decrease is 2.1 %.

Answer 2

700(2)^(-x/33)

= 700(1/2)^(1/33)x= 700(.9792145972^x

only about 98% remains after each time period, so it decays 100%-98% = 2% each time period x

more precisely 97.92% remains, with 2.08% decay = 2.1% rounded to 1 decimal