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1. The given sequence is a geometric sequence.
The nth term of a geometric sequence is given by
where is the nth term of the sequence,
is the first term of the sequence and
r is the common ratio.
In the given sequence,
a₁ = 3 and r = 2
∴ aₙ = 3(2ⁿ⁻¹)
2. All geometric sequences are discrete form of exponential functions.
A geometric sequence is given by
aₙ = a₀ rⁿ , where n is a discrete value, in other words, a counting integer.
If the discrete value, n is replaced by a continuous variable, x , the resulting function is exponential in nature.
3. Here, the given function is f(x) = 3(1.06 x) + 2.
We see that, f(x) increases with increase in x.
Let us assume x to be the amount of gold in grams and f(x) to be the price of gold.
The cost of gold is directly proportional to the amount of gold bought and there is a flat tax collected, which is 2 bucks.
4. Constant rate of change : When a quantity changes uniformly over the another quantity, it is said to constant change over the other. For example, when a car covers a distance of 50 km every hour, the car is said to have a constant speed, which is rate of change of distance.
Average rate of change : It is the average rate at which one quantity is changing with respect to another. Suppose let us take the car to be covering a distance of 50 km in the first hour and 60 km in the second hour. Here, the rate of change in first hour is 50 kmph, where as in the second is 60 kmph. The average rate of change is 55 kmph.
5. Average rate of change is the slope of the function.
Here the function is g(x)=6x-6
If y = mx+c, the slope is m.
Here, the function is also of the same form, where m =6 and c = -6.
So, the slope of the equation is 6.
Average rate of change is 6 in the interval, 0≤x≤3
Panic disorder.
You feel terror that strikes at random. During a panic attack, chest pain, and feel palpitations. Sometimes you may feel like you’re choking or having a heart attack.
Social anxiety disorder:-
Also called social phobia, this is when you feel overwhelming worry and self-consciousness about everyday social situations.
Specific phobias.
You feel intense fear of a specific object or situation, such as heights or flying. The fear goes beyond what is appropriate and may cause you to avoid ordinary situations.
Generalized anxiety disorder.
You feel excessive, unrealistic worry and tension with little or no reason.
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