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:
C
Step-by-step explanation:
calculate like terms, then it is pretty simple from there.
94%
47/50 × 100 = 47 ×2 = 94 %
Answer:
25.85 years
Step-by-step explanation:
Use the formula for continuous compounding amount:
A = Pe^(r*t), where r is the interest rate as a decimal fraction, P is the initial amount, and t is the time in years.
Here we have:
A = $200e^(0.0425*t) = 3($200) (this is triple the original amount)
Solve this for t. Divide both sides by $200 and then use natural logs:
1e^(0.0425*t) = 3
Then 0.0425*t = ln 3 = 1.0986
Dividing both sides by 0.0425 will isolate t:
1.0986
t = --------------- = 25.85 years
0.0425
