Question

1. The ordered pairs model an exponential function, where j is the function name and e is the input variable.

{(1, 10), (2, 50), (3, 250), (4, 1250)}

What is the function equation in sequence notation?

Enter your answer in the box.
je=_______


2. The population of a pack of wolves is 88. The population is expected to grow at a rate of 2.5% each year.

What function equation represents the population of the pack of wolves after t years?

f(t)=88(1.025)^t

f(t)=88(0.025)^t

f(t)=88(2.5)^t

f(t)=88(1.25)^t


3. Ramon bought a bicycle for $478. The value of the bicycle is expected to decrease at a rate of 6.5% each year.

What function equation represents the value of the bicycle after t years?

f(t)=478(1.065)^t

f(t)=478(0.935)^t

f(t)=478(6.5)^t

f(t)=478(0.065)^t

Answer 1

Answer: Hi. I am sorry if this is a late answer, but here are the answer's I have. I just took the test so I am pretty sure these are correct:

#1.

2(5^e)

#3.

B) f(t)=478(0.935)^t

I am so sorry but I don't have the answer for question #2. I hope you figure it out or someone else can help you. I hope I helped. Good Luck!

Answer 2

1)
`j=2(5)^e`

2) option A

3) option B

Explanation:

1) Given: The ordered pairs model an exponential function, where j is the function name and e is the input variable.

{(1, 10), (2, 50), (3, 250), (4, 1250)}

Let an exponential function
`y=ab^x`

Now, put (1,10) ⇒10=ab .....(1)

put (2,50) ⇒
`50=ab^2` ....(2)

divide (1) and (2)

we get b=5 then put back in (1)

we get 10=a(5)⇒ a=10/5= 2

therefore the required function is
`y=2(5)^x`

For j is the function name and e is the input variable

the function is
`j=2(5)^e`

2) Given: The population of a pack of wolves is 88. The population is expected to grow at a rate of 2.5% each year.

To find: What function equation represents the population of the pack of wolves after t years

solution :
`f(t) = P(1+r)^t`

where P-population , r- growth rate , t -time

putting value we get,
`f(t) = 88(1+0.025)^t`

`f(t) = 88(1.025)^t`

therefore, option A is correct

3) Given: Ramon bought a bicycle for $478. The value of the bicycle is expected to decrease at a rate of 6.5% each year.

To find: What function equation represents the value of the bicycle after t years.

solution :
`f(t) = P(1-r)^t`

where P-population , r- decay rate , t -time

putting values we get,
`f(t) = 478(1-0.65)^t`

`f(t) = 478(0.935)^t`

therefore, option B is correct