There are 7 tigers at the zoo. Each year, the number of tigers increases by 10%. There are 15 eagles at the zoo. Each year, 2 new eagles join the zoo.

Part A: Write functions to represent the number of tigers and eagles at the zoo throughout the years. (4 points)

Part B: How many tigers are at the zoo after 10 years? How many eagles are at the zoo after the same number of years? (2 points)

Part C: After approximately how many years is the number of tigers and eagles the same? Justify your answer mathematically. (4 points)

Question

There are 7 tigers at the zoo. Each year, the number of tigers increases by 10%. There are 15 eagles at the zoo. Each year, 2 new eagles join the zoo.

Part A: Write functions to represent the number of tigers and eagles at the zoo throughout the years. (4 points)

Part B: How many tigers are at the zoo after 10 years? How many eagles are at the zoo after the same number of years? (2 points)

Part C: After approximately how many years is the number of tigers and eagles the same? Justify your answer mathematically. (4 points)

dude · Answer

Have you written anything on this before I write anything? xd

Nevey · Answer

no i havent.

dude · Answer

Do you know the general exponential formula?

Nevey · Answer

no

dude · Answer

Since the population of tigers is increased you want to do exponential growth
$y = a(1 + r)^x$

dude · Answer

Does that seem familiar to you?

Nevey · Answer

kinda but not really

Nevey · Answer

@dude

dude · Answer

a is the original amount and the r is the rate at which it increases

Turn 10% into a decimal, do you know how to do that?

Nevey · Answer

its 0.1right?

dude · Answer

Yes

Nevey · Answer

alright

dude · Answer

$y = a(1 + r)^x$

a = original
r = % as decimal

Substitute what we have

Nevey · Answer

y=7(1+0.1)^x

Nevey · Answer

thats part of part a right?

dude · Answer

Ya

Nevey · Answer

ok now what?

dude · Answer

To get part B

Substitute 10 in for x
x = years

$y=7(1+0.1)^x$

dude · Answer

For part C you want to find the equation for eagles at the zoo

This is a linear growth

$y=mx+b$
m is the rate 
b is the original amount

dude · Answer

`There are 15 eagles at the zoo. Each year, 2 new eagles join the zoo.`

dude · Answer

From there you want to set both equations equal to each other
$y=7(1+0.1)^x$ and (the equation you get from above)

Nevey · Answer

y = 2x + 15
y=7(1+0.1)^10
@dude do i just stop there?

dude · Answer

$\color{#0cbb34}{\text{Originally Posted by}}$ @dude
From there you want to set both equations equal to each other
$y=7(1+0.1)^x$ and (the equation you get from above)
$\color{#0cbb34}{\text{End of Quote}}$

Nevey · Answer

I know, i read that, but is that not what i did :/ im confused. what do i do after putting one equation above the other?

dude · Answer

Set them equal
$7(1+0.1)^x=2x+15$

Then solve for x

Nevey · Answer

well, the first equation is equal to 17. i did that in part B. so i just solve the equation to find how many eagles right?

dude · Answer

No no you’re solving for them individually, you want to get the x on the same side

Nevey · Answer

oh wait lol now i get it. ok sorry :)

Nevey · Answer

@dude this is what i got. is it right?

Nevey · Answer

well i have to turn it in now. thank you so much for your help. i will just hope its all correct. :)

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