hectictar

num of people after   0   years   =   2000

num of people after  10  years   =   2000(1 + 0.014)¹⁰   =   2000(1.014)¹⁰

The number you calculated is the population after 10 years...now we need the avg rate of change.

avg rate of change   =   \(\frac{\text{change in num of people}}{\text{change in num of years}}\)

avg rate of change   =   \(\frac{2000(1.014^{10})\,-\,2000}{10\,-\,0}\)     people/year

avg rate of change   ≈   29.831   people/year     ≈     30 people/year   

Well....I'm pretty sure it's right, but....my answer still hasn't been validated with a checkmark!

arc length / circumference   =   central angle in radians / ( 2π )

arc length / ( 2π * 63 )   =   ( 2π/9 ) / ( 2π )

arc length   =   ( 2π/9 ) / ( 2π )  *  ( 2π * 63 )

arc length   =   2π/9  *  63

arc length   =   14π    centimeters

(a)

So

our result   =   5(2 - 8) + \(\frac12\)(12 * 8 - 24)   =   -30 + 36   =   6

(b)

Notice that no matter what number we chose to begin with,

we can calculate our result with this equation:

result   =   5(2 - x) + \(\frac12\)(12x - 24)    , where  x  is the number we chose.

                                                         Let's simplify this and solve for  x .

result   =   10 - 5x + 6x - 12

result   =   x - 2

                               Add  2  to both sides of the equation.

result + 2   =  x

                               In other words...

the number we chose   =  our result + 2  .

To find the number we chose, MathWizard adds  2  to our result.

Notice that  ∠BCH  and  ∠HCD  form a straight line, so they must add to  180° .

∠BCH  +  ∠HCD   =   180°

And...

m∠HCD  =  (3x + 13)°        CPhill already found that  x = 9 , so that means

m∠HCD  =  (3(9) + 13)°

m∠HCD  =  (27 + 13)°

m∠HCD  =  40°

So.....remember...

∠BCH  +  ∠HCD   =   180°

∠BCH  +     40°     =   180°

Can you finish it from here? 

They eat cake on July 27, July 28, July 29, July 30, and July 31.  That is  5  days.

They eat cake every day in August.  That is  31  days.

They eat cake on Sept 1, Sept 2, and Sept 3.  That is  3  days.

the number of cake-eating days per year   =   5 + 31 + 3   =   39

They do this in the years  '08 , '09 , '10 , '11 , '12 , '13 , '14 , '15 , and  '16 .  That is  9  years.

39 cake-eating days per year  *  9 years   =   351 cake-eating days

1 + 1  =   2   

Does this answer your question?

I think we need more information. Where is point  D  or point  E ?

So far, this is all we know....

1.

When   x = -2 ,   f(x) = 4   and   g(x) = 4   so when   x = -2 ,   f(x) = g(x) .

When   x = -1 ,   f(x) = 2   and   g(x) = 2   so when   x = -1 ,   f(x) = g(x) .

None of the other values for  x  make  f(x) = g(x) .

2.

The solutions to   -2x + 2  =  (1/3)^x + 1   are the solutions to  f(x) = g(x) .

When   x = -1 ,   f(x) = 4   and   g(x) = 4   so when   x = -1 ,   f(x) = g(x) .

When   x = 0 ,   f(x) = 2   and   g(x) = 2   so when   x = 0 ,   f(x) = g(x) .

None of the other values for  x  make  f(x) = g(x) .