35) If the interest earned on a sum of money invested for 3 years at the annual interest rate of \( 10 \% \) compounded annually is \( ₹ 14,895 \), then what is the sum of money invested?

3: Exponential and Logarithmic Functions hework: Solving with and without Logarithms If you deposit \( \$ 6500 \) into an account paying \( 8 \% \) annual interest compounded monthly, how much money will be in the account after 7 years?

The formula for simple interest is \( I=P r t \), where \( P= \) principal, \( r= \) rate, and \( t= \) time. Solve the formula for \( r \). \( \begin{array}{l} r=\frac{t I}{P} \\ r=\frac{P t}{l} \\ r=\frac{P I}{t} \\ r=\frac{l}{P t}\end{array} \)

If \( x \) represents the number of items produced, (a) write a cost function, (b) find a revenue function if each item sells for the price given, (c) state the profit function, (d) determine analytically how many items must be produced before a profit is realized (assume whole numbers of items), and (e) support the results of part (d) graphically. The fixed cost is \( \$ 500 \), the cost to produce an item is \( \$ 20 \), and the selling price of the item is \( \$ 45 \). (a) The cost function is \( \mathrm{C}(\mathrm{x})=\square \). (Simplify your answer. Do not factor.) (b) The revenue function is \( \mathrm{R}(\mathrm{x})=\square \). (Simplify your answer. Do not factor.) (c) The profit function is \( \mathrm{P}(\mathrm{x})=\square \). (Simplify your answer. Do not factor.) (d) At least \( \square \) items must be produced before a profit is shown. (Type a whole number.) (e) Choose the correct graph to the right.

A family has a monthly income of \( \$ 3100 \) and plans to spend \( 7 \% \) of this amount on entertainment. How much will be spent on entertainment? The family will spend \( \$ \square \) on entertainment.

You deposit \( \$ 1000 \) each year into an account earning \( 3 \% \) interest compounded annually. How much will you have in the account in 25 years? \( \$ \)