Answer:
37.5 °C
Step-by-step explanation:
The temperature appears to be increasing linearly at the rate of 5 °C in 2 minutes, or 2.5 °C per minute.
1 minute after 4 minutes, when the temperature is 35 °C, we expect it to be 2.5 °C higher, or 37.5 °C.
Answer:
Exponential decay.
Step-by-step explanation:
You can use a graphing utility to check this pretty quickly, but you can also look at the equation and get the answer. Since the function has a variable in the exponent, it definitely won't be a linear equation. Quadratic equations are ones of the form ax^2 + bx + c, and your function doesn't look like that, so already you've ruled out two answers.
From the start, since we have a variable in the exponent, we can recognize that it's exponential. Figuring out growth or decay is a little more complicated. Having a negative sign out front can flip the graph; having a negative sign in the exponent flips the graph, too. In your case, you have no negatives; just 2(1/2)^x. What you need to note here, and you could use a few test points to check, is that as x gets bigger, (1/2) will get smaller and smaller. Think about it. When x = 0, 2(1/2)^0 simplifies to just 2. When x = 1, 2(1/2)^1 simplifies to 1. Already, we can tell that this graph is declining, but if you want to make sure, try a really big value for x, like 100. 2(1/2)^100 is a value very very very veeery close to 0. Therefore, you can tell that as the exponent gets larger, the value of the function goes down and gets closer and closer to zero. This means that it can't be exponential growth. In the case of exponential growth, as the exponent gets bigger, your output should increase, too.
Answer:
26 bags
Step-by-step explanation:
A bag of cat chows = 30 lbs
Amount of cat chows needed in a week = 15 lbs = ½ bag of cat chow
There are at least 52 weeks in a year.
The least number of cat chows bags needed at the shelter in 1 year = 52 weeks × ½ bag of chow
= 52 × ½
= 52/2
= 26 bags of cat chow
At least, 26 bags would be needed in 1 year (52 weeks) at this wild life shelter if 15 lbs is consumed weekly.
Answer: both the left and right sides go to +∞
<u>Step-by-step explanation:</u>
End behavior can be determined by two things:
- Sign of the leading coefficient
- Degree of the function
<u>Sign of leading coefficient</u>:
positive: right side goes to +∞
negative: right side goes to -∞
⇒ Leading coefficient of this function is 3 so the right side goes to +∞
<u>Degree (exponent of leading coefficient)</u>:
even: both the left and right sides point in the SAME direction
odd: the left and right sides point in OPPOSITE directions
⇒ Degree of this function is 4 so the left side will point in the same direction as the right side.
Answer:
figure skates will be $1 cheaper.
Explanation:
<u>given equation</u>:
- to rent figure skates : f(x) = 1.50x + 2
- to rent hockey skates : h(x) = 2x +1.5
<u>solve for rent of figure skates</u>:
f(x) = 1.50x + 2.00
f(3) = 1.50(3) + 2.00
f(3) = 6.5
<u>solve for rent of hockey skates</u>:
h(x) = 2x + 1.5
h(3) = 2(3) +1.5
h(3) = 7.5
<u>cheaper - figure skates than hockey skates</u>:
$7.5 - $6.5
$1
