Lesson 2: Exponential Models — Practice Questions

1. 1. Find an exponential function $f(x) = ab^x$ that passes through the points $(2, 9)$ and $(3, 12)$. The function is $f(x) = \_\_\_$.

2. 2. Find the equation of the line that passes through the points $(0, 4)$ and $(2, 3)$.

   • A. $y = -\frac{1}{2}x + 4$
   • B. $y = -2x + 4$
   • C. $y = \frac{1}{2}x + 3$
   • D. $y = -x + 4$

3. 3. Solve for $x$: $2x^2 - 4.7x = 3.8$. Round your answers to the nearest hundredth.

   • A. $x \approx 2.99$ and $x \approx -0.64$
   • B. $x \approx 3.12$ and $x \approx -0.77$
   • C. $x \approx -2.99$ and $x \approx 0.64$
   • D. $x \approx -3.12$ and $x \approx 0.77$

4. 4. Find an exponential function $P(t) = ab^t$ that passes through the points $(0, 8)$ and $(5, 0.25)$. The function is $P(t) = \_\_\_$.

5. 5. Solve for $x$. Round your answer to the nearest hundredth. $4.6(x - 3)^{1.8} + 12 = 18$. \newline $x = \_\_\_$

6. 6. Find the equation of the line with a slope of $-\frac{2}{3}$ and a y-intercept of $(0, -1)$.

   • A. $y = -\frac{2}{3}x - 1$
   • B. $y = \frac{2}{3}x - 1$
   • C. $y = -\frac{2}{3}x + 1$
   • D. $y = \frac{3}{2}x - 1$

7. 7. Find the equation of the line that passes through the points $(-3, 0)$ and $(0, -5)$.

   • A. $y = -\frac{5}{3}x - 5$
   • B. $y = \frac{5}{3}x - 5$
   • C. $y = -\frac{3}{5}x - 5$
   • D. $y = -\frac{5}{3}x + 3$

8. 8. Find the equation of the line with a slope of $-2$ that passes through the point $(-1, 2)$.

   • A. $y = -2x$
   • B. $y = -2x + 4$
   • C. $y = 2x + 4$
   • D. $y = -2x - 4$

9. 9. An investment of 500 dollars is made in an account with 9.5% interest compounded continuously. How many years will it take for the investment to double? Round to two decimal places. The amount is given by $A(t) = Pe^{rt}$. $\_\_\_$ years.

10. 10. A principal of 3000 dollars is invested at an annual rate of 5% compounded continuously. What is the total amount after 10 years? Round to the nearest cent. ___