Question

Given the following exponential function, identify whether the change represents

growth or decay, and determine the percentage rate of increase or decrease.
y = 940(1.89)

Answer 1

Answer: The change represents growth with 89% of growth rate.

Explanation:

The exponential function is given by :-

`f(x)= Ab^x`... (i)

Where , A = initial value , b= multiplicative factor and x= time period

• We call 'b' growth factor when b>1, we can write b= 1+r , where r is the rate of growth.

• We call 'b' decay factor when b<1 , we can write b= 1-r , where r is the rate of decay.

The given function :
`y = 940(1.89)^x`.

By comparing this to (i) , we get

b= 1.89 > 1 , thus it represent the growth.

Also,

`b= 1+r\Rightarrow\ 1.89 = 1+r\\\\\Rightarrow\ r=1.89-1=0.89`

i.e. Percentage rate of growth = 0.89 x 100 = 89%.