The number of exercises on Khan academy has increased rapidly since it began in 2006The relationship between the elapsed time, ttt, in years, since Khan academy began, and the total number of its exercises, E_{\text{year}}(t)E year

(t)E, start subscript, start text, y, e, a, r, end text, end subscript, left parenthesis, t, right parenthesis, is modeled by the following function:
Eyear(t)=100⋅(1.7)t
Complete the following sentence about the monthly rate of change in the number of exercises.
Round your answer to two decimal places.
Every month, the number of exercises increases by a factor of

1.05

Step-by-step explanation:

We start of with 100 * (1.7)^t

So the change in 100 is (1.7)^t(years). Well, that is in years, we need months. There are 12 months in a year, this is good to remember for several reasons ;). Since they ask for "Every month, the number of exercises increases by a factor of:", we must plug in 1/12 as t.

We can rewrite this as:

100 * (1.7)^1/12

Just plug the (1.7)^1/12 into a calculator, which is a cool device that can do boring math for you, and you should get 1.045... blah blah blah(a bunch of other useless numbers).

So now we have:

100*1.045

Well, the problem said "Round your answer to two decimal places."

So we need to round the 1.045.

5 is right in the middle, but if you know rounding, your probably know that the 5 goes up. So yay, your 1.045 is now 1.05.

So in the end, we get:

1.05

Ti⊂k∫∈s ω∅∅p :)

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

answer: 298143

step-by-step explanation: