In recent years, the number of people in a certain country who are 100 years old or older can be estimated by the function p(t) = 1.32t − 2589.6
where
t = the year
p(t) = the number of people, in thousands, who are 100 or older.
(See Example 4.)
(a) Find p(2015)
p(2015) = thousand

Find p(2025)
p(2025) = thousand

(b) Use the function to estimate when the number of people 100 years or older will reach 100,000. (Round your answer to the nearest year.)

See below for answers

Step-by-step explanation:

(a) Substitute t=2015 into the function:

p(t) = 1.32t - 2589.6

p(2015) = 1.32(2015) - 2589.6

p(2015) = 2659.8 - 2589.6

p(2015) = 70.2

So, there will be 70,200 people in 2015 who will be 100 years or older.

Substitute t=2025 into the function:

p(t) = 1.32t - 2589.6

p(2025) = 1.32(2025) - 2589.6

p(2025) = 2673 - 2589.6

p(2025) = 83.4

So, there will be 83,400 people in 2025 who will be 100 years or older.

(b) Substitute p(t)=100 into the function and solve for t:

p(t) = 1.32t - 2589.6

100 = 1.32t - 2589.6

2689.6 = 1.32t

2037.57 = t

2038 = t

Therefore, the number of people 100 years or older will reach 100,000 by 2038.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."