Calculus Test 3

In a certain environment, a colony of bacteria grows according to the model A=A0e^0.32t, where A is the number of bacteria present at time t (in hours) after a culture is taken and A0 is the initial number of bacteria present. If 250 bacteria are initially present, how many bacteria are present after 14 hours? Round your answer to the nearest whole number.

A0=250 t=14 A=250e^0.32(14) =22059

How long does it take for $3675 to double if it is invested at 8.5% compounded continuously? Round your answer to two decimal places.

A=Pe^rt A=2*3675=7350 P=3675 r=0.085 7350=3675e^0.08t

$5900 is invested at 6.0% compounded continuously. How long will it take for the balance to reach $11800? Round your answer to two decimal places

A=pe^rt A=11800 P=5900 r=0.06 11800=5900e^0.06t =11.55

How long does it take for 1625 to double at 8% invested continuously?

A=pe^rt A=2*1625 = 3250 P= 1625, r= 0.08 3250= 1625e^0.08t 8.66

The compound interest formula states that if P dollars are invested at an annual interest rate of r, compounded n times per year, then A, the amount of money present after t years, is given by A=P(1+r/n)^nt. Using this formula, determine how long it will take for $9,000 to double if it is invested at 6.5% compounded quarterly? Round your answer to two decimal places.

P=9000 A= 2*9000=18000 r= 6.5 =0.065 n=4 (quarterly) 18000=9000(1+0.065/4)^4t =10.75

Hattie has recently inherited $9200, which she wants to deposit into an IRA account. She has determined that her two best bets are an account that compounds semi-annually at a rate of 3% (Account 1) and an account that compounds monthly at an annual rate of 5%.(Account 2). How much would Hattie's balance from account 2 be after 5 years? Round to two decimal places

a=9200(1+0.05/12)^12(5) a=9200(1.28335867850351) A= 11806.90

Jeff's father is planning to open a savings account to pay for Jeff's college education. He has found a bank that will pay 8 percent interest compounded weekly. How much will he need to deposit initially so that in 5 years the balance will be $156,000? Round your answer to the nearest cent.

a=p(1+r/n)^nt 156000=p(1+0.08/52)^52*5 p=156000(1+0.08/52)^-260 =104602.07

Find the amount of money that will be accumulated in a savings account if $4600 is invested at 6.0% for 6 years and the interest is compounded continuously. Round your answer to two decimal places.

a=pe^rt p= 4600 r= 0.06 t= 6 a=4600e^0.06(6) =6593.32

give an example of a polynomial function for which F(4)=−20; F′(x) is nonzero; and F″(x)=0 for all x.

equation is f(x)=ax+b, find derivative for equation. f(x)= 0. a must be 4. x=-5

Consider the function f(x)=3x^3−9x on the interval [−9,9]. Find the absolute extrema for the function on the given interval. Express your answer as an ordered pair (x,f(x)).

find derivative of equation. set = to 0 and solve. plug (-9,9) and other intervals into original equation and determine max and min

The cost function for a particular product is given by C(x)=0.001x3−0.24x2+27.9x+180 dollars, where 0≤x≤1000 Find the minimum marginal cost of the product, rounded to the nearest cent.

find the derivative of c(x). find the derivative of the new equation. find the second derivative of this equation. set = to 0 and solve for x. plug x into original m(x) equation.

maximize the revenue from the sale of x units where R(x)=168x−6x2 thousand dollars and 0≤x≤270

find the derivative of equation and set it = to 0 and solve for x plug 0,27, and 14 into original equation and determine max and min

Determine a value for s so that f(x)=sx2−5x+8 has a minimum at x=1

find the derivative of f(x) equation. plug 1 in for x. set the derivative = to 0 and solve for s.

The sales function for a product is given by S(x)=119+23.1x2−0.7x3, where x represents thousands of dollars spent on advertising, 0≤x≤220 and S is in thousands of dollars. Find the point of diminishing returns. Enter the amount spent on advertising as well as the sales in dollars

find the derivative of s(x). find the second derivative of that equation. set it = 0 and solve. plug the new numbers into the original s(x) equation. Total cost is new number plugged in. advertising cost is number found from solving for x. In thousands.

If $11,500 is invested at 10% compounded quarterly, how much will this investment be worth in 3 years? Round your answer to two decimal places.

p= 11500 r=0.01 n=4 t=3 a=p(1+r/n)^nt a=11500(1+0.1/4)^4(3) a=15466.22

The concentration C(t)of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.03(1−e^−0.2t). What is the concentration after 14 minutes? Round to three decimal places

plug 14 in for t and solve.

for f(x)=6^1/2x, find f(7)

plug 7 in for x and solve.

Junker Renovation completely overhauls junked or abandoned cars. Data shows their 1970's models hold their value quite well. The value F(x)F(x) of one of these cars is given by F(x)=95−14x/x+1 where x is the number of years since repurchase and F is in hundreds of dollars. What is the initial resale price of the car?

substitute 0 in for x in the equation and solve.

The weekly revenue from the production and sale of x units of salt is given by R(x)=75x−2x2 thousand dollars. The cost function is given by C(x)=2x2+11x+8 thousand dollars. Find the number of units of salt that are to be produced to maximize the profit if 0≤x≤19

subtract c(x) from r(x). with the new equation, find the derivative and set = to 0. plug 0,19, and the number found from the equation into original p(x) equation. determine max and min