Question

Plz help me!!!

The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.

Answer 1

To solve this we are going to use the exponential function:
`f(t)=a(1(+/-)b)^t`
where

`f(t)` is the final amount after
`t` years

`a` is the initial amount

`b` is the decay or grow rate rate in decimal form

`t` is the time in years

Expression A

`f(t)=624(0.95)^(4t)`
Since the base (0.95) is less than one, we have a decay rate here.
Now to find the rate
`b`, we are going to use the formula:
`b=|1-base|`*100%

`b=|1-0.95|`*100%

`b=0.05`*100%

`b=`5%
We can conclude that expression A decays at a rate of 5% every three months.

Now, to find the initial value of the function, we are going to evaluate the function at
`t=0`

`f(t)=624(0.95)^(4t)`

`f(0)=624(0.95)^(0t)`

`f(0)=624(0.95)^(0)`

`f(0)=624(1)`

`f(0)=624`
We can conclude that the initial value of expression A is 624.

Expression B

`f(t)=725(1.12)^(3t)`
Since the base (1.12) is greater than 1, we have a growth rate here.
To find the rate, we are going to use the same equation as before:

`b=|1-base|`*100%

`b=|1-1.12|`*100

`b=|-0.12|`*100%

`b=0.12`*100%

`b=`12%
We can conclude that expression B grows at a rate of 12% every 4 months.

Just like before, to find the initial value of the expression, we are going to evaluate it at
`t=0`

`f(t)=725(1.12)^(3t)`

`f(0)=725(1.12)^(0t)`

`f(0)=725(1.12)^(0)`

`f(0)=725(1)`

`f(0)=725`
The initial value of expression B is 725.

We can conclude that you should select the statements:
- Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every fourth months.

- Expression A has an initial value of 624, while expression B has an initial value of 725.