Homework Sourse16A company has a stock valued at A in millions of dollars t
16)A company has a stock valued at A, in millions of dollars, that changes at a rate given by da/dx=160.51x^0.4381 , where x is the number of years since the year 2000. If the value of the stock is $ 998.30 million in 2000, find the function that models the total amount of stock company A has and #17)
Evaluate the definite integral Integral symbol [3 on top 2 on bottom](x-3)^5 dx
Evaluate the definite integral Integral symbol [3 on top 2 on bottom](x-3)^5 dx
Solution
16) Well first we take the integral of the equation. f(x)=(160.51/1.4381)x^1.4381+C Now we need to find C. We can do this by inputing f(0)=998.3 f(0)=(160.51/1.4381)0^1.4381+C 998.3=0+C 998.3=C f(x)=(160.51/1.4381)x^1.4381+998.3 17) We can do this by using u subsitution. We can say that x-3=u. du=dx(This is true by differentiating both sides of x-3=u). Now we integrate u^5du which is much easier and we get: u^6/6 or f(x)=(x-3)^6/6 if we plug in f(3)-f(2)=0-1/6=-1/6
