Question

for over 20 years the population of ohio has been increasing linearly according to the function
p(t)= 375+7500
where p is numer of residents and t is years after 1980. compute p(0) and intrepret its meaning in the context of the problem

Answer 1

To find \(p(0)\) simply rewrite the equation for \(p(t)\), substituting \((0)\) wherever you see \(t\). Then evaluate the resulting expression.

If p(t) is the population in year 1980+t, p(0) is the population when?

Answer 2

so 1980+20, 7500?

Answer 3

How do you get that?

Answer 4

write out p(t), except where you see t, write (0). what do you get?

Answer 5

it doesn't look like you've got the right value of p(t) stated in the problem..there's no \(t\) in it!

Answer 6

I suspect it should be \(p(t) = 375t+7500\)

Answer 7

oh yes thats correct sorry

Answer 8

p(0)=375t+7500

Answer 9

is that correct?

Answer 10

well, it's part of the way, I still see a t in there...

Answer 11

you have to go through the entire equation, replacing t with the value of t

Answer 12

p(0)=375(0)+7500

Answer 13

and that evaluates to?

Answer 14

p=7500?

Answer 15

you're not sure? :-)

Answer 16

lol im pretty sure

Answer 17

p(0) = 7500

so how do you interpret that result?

Answer 18

uh i have no clue...

Answer 19

well, look at the problem statement again. t is the number of years since 1980. p(t) is the population. what does that suggest about p(0)?

Answer 20

it's the population in some year. which year?

Answer 21

1980

Answer 22

right!

most growth equations are structured so that p(t) = <initial amount>*(function describing growth)

P(0) = 7500 is the initial amount. The function describing the growth here is 375t.

Answer 23

here we are adding on, not multiplying, but in an exponential growth, like you would have for money accruing compound interest in the bank, or population growth, or radioactive decay it would be multiplication.