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.