Average rate = distance / time
distance = average rate x time
Range of distance = 2.2(1) to 2.2(3) = 2.2 to 6.6
Required range is all real numbers from 2.2 to 6.6, inclusive.
1. The function
is a parabola of the form
. The the formula for the axis of symmetry of a parabola is
. We can infer from our function that
and
, so lets replace those values in our formula:
We can conclude that to the left of the line of symmetry the ball is reaching its maximum height, and to the right of the line of symmetry the ball is falling.
2. Lets check how much time the ball takes to reach its maximum height and return to the ground. To do that we are going to set the height equal to zero:
or
or
From our previous point we know that the ball reaches its maximum time at
, which means that <span>
it takes 1.5 seconds to reach the maximum height and 1.5 seconds to fall back to the ground.</span>
1) Since this is a Continuously Compounded operation in a 10 yrs period, then we can write out the following equation:
2) Plugging into the equation the given data and since Otto is 20 yrs old and he plans to get $4,000 in ten years, we can write out:
3) Thus the rate Otto needs is
Note that since the 0.1386 the six here is greater than 5 then we can round up to the next thousandth, in this case: 0.139. For the 0.1386 is closer to 0.139 (0.004) than to 0.138 (0.006).
Or 13.9%
The value of the digit 4 is worth 4,000 in the number 84,230.