Exponential Functions: math test, Grade 11 – download the PDF

1 Classify and evaluate / 3 pts

1. (1 pt) Classify each function as growth or decay and give the percent rate: \( y = 2.5(1.04)^{x} \) and \( y = 90(0.95)^{x} \).
2. (2 pts) For \( f(x) = 4\left(\tfrac{3}{2}\right)^{x} \), compute \( f(0) \), \( f(2) \) and \( f(-1) \).

2 Transformations and graph / 4 pts

Let \( g(x) = 2^{\,x+1} - 3 \).

1. (1 pt) Describe how to get its graph from \( y = 2^{x} \).
2. (1 pt) Give the horizontal asymptote and the range.
3. (1 pt) Find the y-intercept.
4. (1 pt) Complete a table for \( x = -3, -2, -1, 0, 1 \) and sketch the curve.

3 Equation from two points / 3 pts

An exponential function \( f(x) = a \cdot b^{x} \) passes through \( (1, 12) \) and \( (3, 108) \). Find the formula, then compute \( f(4) \).

4 Compound interest (calculator allowed) / 4 pts

Maria deposits 3,500 dollars at 3.2% for 5 years. (a) Find the balance if interest is compounded quarterly. (b) Find the balance if it is compounded continuously. (c) How much more does continuous compounding earn?

5 A laptop loses value / 3 pts

A laptop costs 1,200 dollars and loses 25% of its value each year. (a) Write \( V(t) \). (b) Find \( V(2) \). (c) In which whole year does its value first fall below 600 dollars?

6 Linking e and money / 3 pts

(a) Compute \( (1.01)^{100} \) to 4 decimal places and compare with \( e \). (b) Find the value of 600 dollars invested for 8 years at 5% compounded continuously.