Wk 6

Sec 12.7 #24
World population growth
In 2008 the world population was 6.7 billion and the exponential growth rate was 1.14% per year.
A.Find the exponential growth function
B.Predict the world’s population in 2014
C.When will the world’s population be 8.0 billion?

Could someone help me with this please?

Growth function:

Assume Y=year, so Y=2008 is year 2008, etc.

The exponential growth function is
N(Y)=N(2008)*1.0114^(Y-2008) for Y≥2008
or
N(Y)=(6.7*10^9)*1.0114(Y-2008)
for Y≥2008

Population at 2014 is therefore
N(2014)=(6.7*10^9)*1.0114(2014-2008)
=7.17*10^9

The population will reach 8 billion when
N(Y)=8*10^9
or
(6.7*10^9)*1.0114(Y-2008) = 8*10^9
1.0114(Y-2008)=8/6.7
Take log on each side and solve for Y:
Y-2008=log(8/6.7)/log(1.0114)=15.6 years
So by the middle of 2023, the world population will reach 8 billions.

Of course! I can help you with that. Let's take it step by step.

A. To find the exponential growth function, we can use the formula:

P(t) = P0 * e^(rt)

Where:
P(t) is the population at time t
P0 is the initial population
r is the growth rate (expressed as a decimal)
t is the time in years

In this case, P0 = 6.7 billion and r = 1.14% = 0.0114 (as a decimal). We can plug these values into the formula to get the exponential growth function:

P(t) = 6.7 * e^(0.0114 * t)

B. To predict the world's population in 2014, we need to substitute t = 6 into the exponential growth function. Doing that gives us:

P(6) = 6.7 * e^(0.0114 * 6)

Now we can calculate the value of P(6) using a calculator or a math software.

C. To find out when the world's population will be 8.0 billion, we can set the exponential growth function equal to 8.0 billion and solve for t:

8.0 = 6.7 * e^(0.0114 * t)

We can solve this equation using logarithms or graphing calculators to find the value of t when the population reaches 8.0 billion.

Let me know if you need further assistance with the calculations!

Of course! I can help you with solving this problem. Let's go step by step.

A. To find the exponential growth function, we need to use the formula:

P(t) = P0 * e^(rt)

Where:
P(t) is the population at a given time t,
P0 is the initial population,
e is Euler's number (approximately 2.71828),
r is the growth rate (expressed as a decimal) per unit of time (in this case per year), and
t is the time elapsed.

In this case, the initial population (P0) is 6.7 billion, and the growth rate (r) is 1.14% per year, or 0.0114 expressed as a decimal. Therefore, the exponential growth function is:

P(t) = 6.7 * e^(0.0114t)

B. To predict the world's population in 2014, we need to substitute t = 2014 - 2008 = 6 into the exponential growth function from part A:

P(2014) = 6.7 * e^(0.0114 * 6)

Using a calculator, calculate e^(0.0114 * 6), multiply it by 6.7, and you will have the predicted world population in 2014.

C. To find when the world's population will be 8.0 billion, we need to solve the exponential growth function for t. Substitute P(t) = 8.0 billion into the exponential growth function from part A and solve for t:

8.0 = 6.7 * e^(0.0114t)

Now, solve this equation for t using algebraic methods or numerical methods (e.g., using a graphing calculator or software). The calculated value of t will give you the year when the world's population is predicted to reach 8.0 billion.