Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The population $P$ at time $t$ of a city is estimated by the equation $P(t)=1500(2)^{-0.25 t}$Suppose $t=0$ corresponds to year $1999, t=1$ to year 2000 and so on. What will be the population in year (a) $2000,$ (b) $2005,$ (c) $2010 ?$

(a) 1261(b) 530(c) 223

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Baylor University

University of Michigan - Ann Arbor

Lectures

02:29

The population $P$ at time…

05:33

The populations $P$ (in t…

08:11

The population $P$ (in tho…

07:06

A city had a population of…

02:06

The population of a city (…

03:47

At time $t,$ the populatio…

04:06

The population $P$ of a ci…

If this equation is supposed to give us the estimated population from 1999 and we want to know it for 2000, 2005 and 2010, then what we'll need to do is first figure out what is going to be t with respect to these years. So, first, 2000 Ah, we would just do, um, that minus 1999 that would give us one for 2000 and five. We would do that minus 1999. Thank you. As a six. For 2010, we would do that minus 1999 which would be 11. So now we're going to take these values and then plug them in to this. So first, we would have 1500 times to raise to the They'll just be negative 0.25 which would be approximately, um, let's see what I got when I plug this in 1261 and I'm just going to round down, then for six, so 1500 to raise to the, um and then it would be negative 0.25 times six, which is going to be negative 1.5. And then if we plug that into a calculator, we should get something around 530 and then last heavy plug in 11 that would give us 1500 times to raise to the negative 2.75 which would be approximately 222. So these over here will be our approximate populations. And so this is for 2000. Or maybe I'll put your first year 2000 and year 2000 and five and then year 2000 and 10. So those are approximate populations.

View More Answers From This Book

Find Another Textbook

Numerade Educator

05:29

Determine the derivative.$$x^{2} e^{2 x^{3} y^{2}}-2 e^{x}+3 e^{2 y}=3 x…

03:27

Sketch the graph of the function defined by the given equation.$$y=f(x)=…

01:08

Determine if the given graph represents a one-to-one function.

02:04

The rate at which an item depreciates is proportional to its value at that i…

03:26

Given the points (2,6) and (4,12) determine the (a) linear function, (b) exp…

03:52

Use the properties of logarithms to find the derivative. Hint: It might be e…

01:25

Solve for $x$ in.$$9^{3 x+2}=27^{2+x}$$

04:09

Sketch the graph of the function defined by the given equation.$$f(x)=\f…

01:09

Determine $f^{\prime}(x)$.$$f(x)=(\ln x)^{5}$$

01:58

Determine the derivative.$$f(x)=\frac{e^{x}+1}{x^{2}-1}$$