Question

Select 2 answers that complete the sentence The exponential function f(x)=100(0.7)^x models And the rate of growth/decay isA exponential growthB exponential decayC 30%D 70%E 130%

Answer 1

Answer:

Given exponential function is,

$f\mleft(x\mright)=100\left(0.7\right)^x$

To find whethere the given function is exponential growth or exponential decay and the rate of growth/decay.

we have that,

In Exponential Growth, the quantity increases very slowly at first, and then rapidly. The rate of change increases over time.The formula to define the exponential growth is:

$y=a\lparen1+r)^x$

where a is the initial number/amount, r is the growth rate.

In Exponential Decay, the quantity decreases very rapidly at first, and then slowly. The rate of change decreases over time. The formula to define the exponential growth is:

$y=a\lparen1-r)^x$

where a is the initial number/amount, r is the decay rate.

Since 0.7 is less than 1, it cannot be exponential growth.

It is exponential decay,

Comparing the given function with exponential decay formula we get,

$\begin{gathered} a=100 \\ 1-r=0.7 \end{gathered}$$\begin{gathered} r=1-0.7 \\ r=0.3 \end{gathered}$

Changing r into percent, we get

$0.3\times100=30\%$

Rate of decay is 30%

Answer is:

The exponential function f(x)=100(0.7)^x models exponential decay and the rate of decay is 30%.