Answer:
Part 1. 0.9259 % per year
Part 2. P = 281.4e^(0.009 259t); 338.6 million
Step-by-step explanation:
Data:
P₀ = 281.4 million
P = 308.7 million
Part 1. Growth rate
t = 2010 - 2000 = 10 yr
P = P₀e^(rt)
308.7 = 281.4e^(10r)
e^(10r) = 1.0970
10r = ln1.0970
r = (ln1.0970)/10 = (0.092 59)/10 = 0.009 259
r = 0.9259 % per year
The 10-year continuous growth rate is 0.9259 % per year.
Part 2. Population model
The population model is
P = 281.4e^(0.009 259t)
where P is in millions and t is the number of years since 2000.
By 2020,
P = 281.4e^(0.009 259 × 20) = 281.4e^0.1852 = 281.4 × 1.203
P = 338.6 million
The estimated population in 2020 is 338.6 million.
Answer:
John and Pam are paid $8.5 for each hour worked. John's share of the money is $29.75.
Step-by-step explanation:
Let x = the hourly salary. John worked for 3.5 hrs, and Pam for two. We can represent this using the equation:
3.5x + 2x = 46.75, where the coefficients equals the amount of hours.
Let's solve for x!
5.5x=46.75
x = 46.75/5.5 = 17/2 = 8.5
John and Pam are paid 8.5 dollars per each hour worked.
To figure out John's share of the money, we will multiply the wage by the hours he worked.
8.5 x 3.5 = 29.75
Your question answers itself. You solve by graphing.
I like to subtract one side of the equation from the other, so the solutions are where the graph crosses the x-axis (the resulting function value is zero).
It can be useful to find the "turning point" of each absolute value expression (where its value is zero) and graph that and some points on either side.
Answer:
x = 31
Step-by-step explanation:
The 2 sides are congruent, meaning the 2 angles are equal so:
47 = x + 16
subtract 16 from both sides
31 = x
