Question

A social networking site currently has 7,000 actiave memembers.if the site loses 5% of its active members, each month, determine the range and domain of this situation​

Answer 1

see the explanation

Explanation:

we know that

The equation of a exponential decay function is equal to

`y=a(1-r)^x`

where

y is the number of active members

x is the number of months

a is the initial value (y-intercept)

r is the rate of change

we have

`a=7,000\\r=5\%=5/100=0.05`

substitute

`y=7,000(1-0.05)^x`

`y=7,000(0.95)^x`

The domain of the function is the interval [0,∞)

`x\geq 0`

Remember that the number of months cannot be a negative number

Te range of the function is the interval (0,7,000]

`0 < y \leq 7,000`