You can see how this works by thinking through what's going on.
In the first year the population declines by 3%. So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200. 3% of 1200 is the same as .03 * 1200. So the population at the end of the first year is 1200 - .03 * 1200. That can be written as 1200 * (1 - .03), or 1200 * 0.97
What about the second year? The population starts at 1200 * 0.97. It declines by 3% again. But 3% of what??? The decline is based on the population at the beginning of the year, NOT based no the original population. So the decline in the second year is 0.03 * (1200 * 0.97). And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year. So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.
So there's a pattern. If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.
So the population after x years is 1200 * 0.97x
Answer: The function is M(t) = 40mg*0.992^t
Step-by-step explanation:
Half life refers to the time that a given quantity to reduce to half its initial value.
This is usually a exponential decay, so we want a function of the form:
M(t) = A*r^(*t)
Were t is time, in this case, t is the number of days
A is the initial value
r is the rate of decrease, we will find that for exponential decays r must be a number between 0 and 1. If r is closer to 0, we will have a fast exponential decay, if r is closer to 1 we will have a slower exponential decay.
We have that the initial mass is 40mg, this is at t = 0.
M(0) = A*r^(0) = A = 40mg
So now we have the value of A.
Now, we know that in t = 84, the mass of the substance will be half its initial value, so it will be:
A/2 = 40mg/2 = 20mg
this means that:
M(84) = 40mg*r^(84) = 20mg
r^(84) = 20mg/40mg = 1/2
= 0.992
Then the equation is:
M(t) = 40mg*0.992^t
Answer:
x³ - 2x² + 2x - 2
Step-by-step explanation:
f(x) - g(x)
= 2x³ - 4x² + 2 - (x³ - 2x² - 2x + 4) ← distribute by - 1
= 2x³ - 4x² + 2 - x³ + 2x² + 2x - 4 ← collect like terms
= x³ - 2x² + 2x - 2