alg 2 help. please. functions?

Question

From 1940 through 1996 in the United States, the age to which a newborn can expect to live can be modeled by

f(t) = 1.78 radical t - 0.3 + 62.7
(radical is supposed to be over t - 0.3)

where t is the number of years since 1940. Graph the model. In what year was the life expectancy at birth 75.7 years?

how do i graph this

Answer 1

The easiest way is to simply plug in some points and get an idea what it looks like...

A square-root curve looks starts low, then goes up a little fast and slows down it's rise....Sort of like a parbola that's been turned on it's side and opens to the right instead of opening up or down. Of course, we only see the top half here in Quadrant I.

In this case, pick some points you know will give the shape of the curve and make an In/Out chart:

Pick T=0, T=1, T=2, T=3, T=4, T=5, T=10, T=20, T=30, T=40 T=50, T=66 and just substitute and evaluate. Plot those points:

IN OUT
0 62.7
1 64.2
2 65.0
And so on...

Connect the dots on your graph with a nice smooth curve and then find 75.7 years on your Y-axis and trace over to where it intersects the curve - That's your answer. (Hint - It's around 50 years).

You can verify your answer by solving the equation:
75.7 = 1.78 * Sqrt(t-.3) + 62.7
Subtract 62.7 from both sides...
13=1.78*Sqrt(t-3)
Divide both sides by 1.78...
7.3=Sqrt(t-3)
Square both sides....and I'll leave the rest as an excersise for the student. :-)

Good luck!

Orion

Answer 2

You do an identical element which you probably did with f(5) in straight forward terms as a replace of changing the x you will replace the f(x) so the equation is going to look like this: 10=sqrt(x+4) to remedy this you may possibly be able to desire to sq. the two factors so which you get: a hundred=x+4 x=ninety six