the population of a city can be modeled using the equation p=40,000x(9/10)^x. one year the population was 23620. what was the following population a year later.
So let's solve
40,000x(9/10)^x = 23620
I will assume that the x after 40,000 is supposed to be a multiplication sign and not a variable,
If it is a variable you have an completely ridiculously hard equation to solve,
If we take it as
40,000(9/10)^x = 23620
then x = 5 is a solution, (too nice not be be that way)
so we want the population when x = 6
P = 40000((9/10)^6
= 21258
o i get it thank you
To find the population of the city a year later, we can substitute the given population value into the equation and then evaluate it for x+1. Let's solve step by step:
Step 1: Substitute the given population value into the equation:
p = 40,000 * (9/10)^x
23,620 = 40,000 * (9/10)^x
Step 2: Solve for x:
Divide both sides of the equation by 40,000.
(9/10)^x = 23,620 / 40,000
Step 3: Take the logarithm of both sides:
Since the base is not specified, we can use the natural logarithm (ln).
ln((9/10)^x) = ln(23,620 / 40,000)
Step 4: Apply the logarithm properties:
Using the power rule of logarithms, we can bring down the exponent:
x * ln(9/10) = ln(23,620 / 40,000)
Step 5: Solve for x:
Divide both sides of the equation by ln(9/10).
x = ln(23,620 / 40,000) / ln(9/10)
Step 6: Evaluate x:
Using a calculator or math software, calculate the value of x.
Step 7: Determine the population a year later:
Substitute the value of x+1 into the equation to find the population.
p = 40,000 * (9/10)^(x+1)
By following these steps, you can determine the population of the city a year later.