1. A population of tropical fish is decreasing at an annual rate of 6% per year.
1 answer:
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Answer:
1. . Exponential decay function.
2. . Exponential growth function.
3. . Exponential growth function.
4. . Exponential growth function.
5. . Exponential growth function.
6. . Exponential decay function.
7. g(x) = 0.3(x). Not an exponential function.
Step-by-step explanation:
1. . This is an exponential decay function.
As the value of t increases H-value decreases.
2. . This is an exponential function of growth.
As the value of t increases y-value also increases.
3. . This is an another example of exponential growth function.
As the value of t increases f(t)-value also increases.
4. . This is again an example of exponential growth function.
As the value of t increases A-value also increases.
5. . This is again an example of exponential growth function.
As the value of t increases A-value also increases.
6. . This is another an example of exponential decay function.
As the value of t increases, H-value decreases.
7. g(x) = 0.3(x). This is a non-exponential function. (Answer)
I know you didn't want an explanation, but I'll give you one anyway.
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
+ 3. Now, plug in the numbers given for s and solve.
1. f(5) = <span> + 3 Plug in 5 for x
</span> =
+ 3 Make three into a fraction over 2
= + <span>
Add
= </span><span><span>
</span>2. f(-4) = </span><span> + 3 Plug in -4 for x
= </span><span>
+ 3 Divide -4 by 2
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2
So, for a function, when you have f(5) = , then you'll put that 5 in for all of the x's in the function.
The first batch of problems gave you the equation f(x) =
1. f(5) = <span>
</span> =
=
= </span><span><span>
</span>2. f(-4) = </span><span>
= </span><span>
= -2 + 3 Add
= 1
For the next set, you have g(x) = x</span>² + 1.
3. Let's split this up. Solve the first equation, then the second, and then put the answers together to solve it.
g(4) = x² + 1 Plug in 4 for x
= 4² + 1 Square
= 16 + 1 Add
= 17
g(3) = x² + 1 Plug in 3 for x
= 3² + 1 Square
= 9 + 1 Add
= 10
Now, put the two together.
g(4) + g(3) = Substitute in the answers you just got.
17 + 10 = Add
= 27
4. g(-1) = x² + 1 Substitute in -1 for x
= (-1)² + 1 Square
= 1 + 1 Add
= 2
5. g(-6) = x² + 1 Plug in -6 for x
= (-6)² + 1 Square
= 36 + 1 Add
= 37
For the last set, we have h(x) = x² + 7 and k(x) = 4x - 5. We'll have to pay close attention to the starting variables here.
6. h(-6) = x² + 7 Plug in -6 for x
= (-6)² + 7 Square
= 36 + 7 Add
= 43
k(4) = 4x - 5 Plug in 4 for x
= 4(4) - 5 Multiply
= 16 - 5 Subtract
= 11
Put the two answers into the final equation.
h(-6) + k(4) = Substitute in the answers you got
43 + 11 = Add
= 54
7. k(10) = 4x - 5 Plug in 10 for x
= 4(10) - 5 Multiply
= 40 - 5 Subtract
= 35
h(2) = x² + 7 Plug in 2 for x
= 2² + 7 Square
= 4 + 7 Add
= 11
Now, put those into the equation.
k(10) - h(2) = Plug in the answers you got
35 - 11 = Subtract
= 24
8. For this one, it wants you to add h(x) and k(x). We don't need to plug anything into the equations this time because they're both already solved for x! So, you can just set this up like a standard find-x equation.
(x² + 7) + (4x - 5) =
x² + 7 + 4x - 5 = Combine like terms (7 and -5)
x² + 2 + 4x = Reorder so the variables come first
= x² + 4x + 2