8.Joe invests $2,500 in a savings account with an interest rate of 4.5%, compounded continuously. (a)Find an equation to represent the amount of money in Joe’s account as a function of time. (b)Find the doubling time for Joe’s account.(c)At what time will Joe’s account hold $3500? (d)Now assume Joe’s account compounds annually instead. Repeat a and c.9. Find an equation for an exponential function between the points (1, 6) and (3, 13.5). 10. Use the table to find ))1((gfx -1 0 f(x) 3 4 g(x) 0 1 . 1 2 5 6 -1 2
11. 23)(xxf7)(xxgGive an equation for ))((xgf12.A cost function for sneakers is given by 𝐶 = 25𝑞 + 1740, where q is the number of pairs of sneakers the company sells. The company sells sneakers for $55. (a)Find an equation for revenue, R, as a function of q(b)Find an equation for profit, π, as a function of q(c)What is the break-even point? How many pairs of sneakers must the company sell to make a profit? 13. A company has fixed costs of $45,000 and variable costs of $9 per item they produce. Find an equation for the company’s total cost.14.The demand for a product is given by 2512pq. Write an equation for revenue as a function of price, p . . . .
15.A bookstore has a linear demand function for stationery. When the price of note cards is $5, the store sells 92 packages. When the price is $8, the supplier sells 68 packages. (a)Find an equation for the demand. (b) Assume the supply function is given by pq14. Find the equilibrium price and quantity. 16. 53)(xxf(a)Is f(x)a power function? (b) Write an equationfor a new function, g(x), which obtained by performing the following operations on f(x)in succession: 1. Stretch by a factor of 342. Shift left 4 units. 3. Reflect across the x-axis. 4. Shift up 7 units. 17.The supply curve for coffee is given by 1318pq, and the demand curve is given by 5315pqwhere pis in dollars and qis cups of coffee. Find the equilibrium price and quantity. .
18. Contract )] 6 ln( )) 3 ln( ) 5 [(ln( 2 to a single logarithm. 19. Solve for x . Round to 3 decimal places. (a) 5? 2𝑥 = 10? 7𝑥
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