The axis of symmetry is -2
Answer:
p(t) = 5*2^t
Step-by-step explanation:
We can solve for 'a' and 'b' using the point coordinates shown on the graph.
<h3>Setup</h3>
Substituting for (t, p(t)), the two equations we can make from the given points are ...
p(t) = a*b^t
5 = a*b^0 . . . . . . . (t, p(t)) = (0, 5)
10 = a*b^1 . . . . . . . (t, p(t)) = (1, 10)
<h3>Solution</h3>
The first equation tells you ...
5 = a
The second equation tells you ...
10 = 5*b
2 = b
<h3>Equation</h3>
The function is ...
p(t) = a*b^t
p(t) = 5*2^t
The area of a square is the square of the length of its side. Here, we're told that the side of each square is equal to the radius (r) of the circle. Then the area of each square is
.. Asquare = r^2
There are 3 of them, so their total area is
.. Aall_squares = 3*r^2
The area of a circle is given by the formula
.. Acircle = π*r^2 . . . . . where r represents the radius of the circle
Fernie wants to compare the area of the 3 squares to that of the circle. We know that the value of π is about 3.1416, a little more than 3, so we have
.. Aall_squares = 3*r^2
.. Acircle ≈ 3.1416*r^2
We notice that 3.1416 is more than 3, so the area of the circle is greater than the area of Fernie's 3 squares.
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It is not clear to me that Fernie's drawing will explain the formula A = π*r^2, unless it can somehow be used to show that the parts of each square that are outside the circle add up to an amount that is slightly less than the uncovered part of the circle.
Sounds like "exponential decay" is the answer your teacher is looking for
Expressions of the form y = a*b^x are considered decay equations or exponential decay equations if 0 < b < 1. So b can be between 0 and 1, but not equal to either endpoint.
Example: y = 3*0.5^x means we start off with 3 as the initial value, and then cut it in half repeatedly as x increases by 1 (eg: x = 0, x = 1, etc). This graph goes downhill as you read it from left to right.
Answer: 8 years
Step-by-step explanation:
You can find this out use the Rule of 72. By dividing 72 by the fixed interest rate, you can estimate the amount of time it will take for an investment to double in size:
= 72/10
= 7.2 years
= 8 complete years
Example:
Assume they invested $1,000. Interest rate is 10%.
Amount after 8 years will be:
= 1,000 * (1 + 10%)⁸
=$2,143.59
<em>Investment is now more than double. </em>
