WILL GIVE BRAINLIST IN SECONDS!!! [ solve for x ]
1 answer:
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Answer:
Step-by-step explanation:
Given that during the period from 1790 to 1930, the US population P(t) (t in years) grew from 3.9 million to 123.2 million. Throughout this period, P(t) remained close to the solution of the initial value problem.
a) 1930 population is the population at time t = 40 years taking base year as 40
We can solve the differential equation using separation of variables
Resolve into partial fractions
Integrate to get
ln P -0.00474/0.0001489 (ln (0.0001489P-0.03135) = t+C
ln P -31.833 (ln (0.0001489P-0.03135) =t+C
Limiting population would be infinity.
2. means that for every x, there is eactly one y
basically, we can use the vertical line test to see if it crosses at any 2 points
first one works
2nd one works
3rd works
4th works
5th works
they are all one to one functions
3.
easy
steps
for f(x)=?
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
so
replace
switch
solve
![\sqrt[3]{x+2}=1+y](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Bx%2B2%7D%3D1%2By)
![-1+\sqrt[3]{x+2}=](https://tex.z-dn.net/?f=-1%2B%5Csqrt%5B3%5D%7Bx%2B2%7D%3D)
replace
![f^{-1}(x)=-1+\sqrt[3]{x+2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D-1%2B%5Csqrt%5B3%5D%7Bx%2B2%7D)
first option
4.
domain, hmm we can't divide by 0 so domain is all real numbers except for x=0
domain is
hmm, range
as x approaches negative or positive infinity, f(x)=5
as x approaches 0 from the left, f(x) appraoches negative infintiy
as x approaches 0 from the right , f(x) appraoches positive infintiy
so range is
domain is
range is
answer is the 4th option
basically, we can use the vertical line test to see if it crosses at any 2 points
first one works
2nd one works
3rd works
4th works
5th works
they are all one to one functions
3.
easy
steps
for f(x)=?
replace f(x) with y
switch x and y
solve for y
replace y with f⁻¹(x)
so
replace
switch
solve
replace
first option
4.
domain, hmm we can't divide by 0 so domain is all real numbers except for x=0
domain is
hmm, range
as x approaches negative or positive infinity, f(x)=5
as x approaches 0 from the left, f(x) appraoches negative infintiy
as x approaches 0 from the right , f(x) appraoches positive infintiy
so range is
domain is
range is
answer is the 4th option