Unit 5: Exponential Functions Review #1

Basic definitions - choose best words to fit in the blanks. The type of function y=a(b)^x represents is exponential function.The function y=a(b)^x models exponential growthwhen b>1.The function y=a(b)^x models exponential decaywhen 0<b<1.An asymptote is an imaginary line that the function approaches, but never crosses. Every exponential function has a horizontal asymptote at y=0, unless it has a vertical shift. Reminders about growth vs decay. Exponential GROWTH increasesas you read the graph from left to right. If a situation is increasing by a percent change, exponential growth can be written as y=a(1+r)^xwhere r is the percent as a decimal.Exponential DECAY decreasesas you read the graph from left to right. If a situation is decreasing by a percent change, exponential decay can be written as y=a(1-r)^xwhere r is the percent as a decimal. Sort based on exponential growth vs decay. Exponential Growth y=0.2(5)^x y=-4(7 Exponential Decay y=100(3 y=(1-r)^x Match the numbers with the vocabulary terms for the following equation:y=3(1.61)x Initial Value (a) 3 Rate Factor (b) 1.61 Rate (decimal) 0.61 Rate % 61% Match the numbers with the vocabulary terms for the following equation:y=23(0.61)x Initial Value (a) 23 Rate Factor (b) 0.61 Rate (decimal) 0.39 Rate % 39% The equation v(t)=12,000(0.75)t represents the value of a motorcycle t years after it was purchased. Which of the following statements is true?Mark all that apply. The motorcycle cost $9,000 when it was purchased The motorcycle cost $12,000 when it was purchased. The motorcycle's value is decreasing by 25% each year. The motorcycle's value is decreasing by 75% each year. What is the rate percent for the equation below?y=5(1.1)x 1.1% 0.1% 10% 1% What is the rate percent for the equation below?y=8(0.27)x 27% 0.27% 73% 0.73% Type the equation and solve: If a bacteria doubles every 30 minutes, and there are 40 bacteria at the beginning, how many will there be in 2 hours? Type the equation and solve: A BTS shirt signed by the band members will become more valuable over time. The initial cost of the concert shirt is $45 and has a 22% growth rate. How much will it be worth in 30 years? Type the equation and solve: A new car cost 18,000 dollars and loses value at 7% per year. How much will the car be worth after 13 years? Compound and Continuous Interest For answers, in order to be marked correct make sure it is in this form:$123.12 (dollar sign and rounded to 2 decimals - no spaces) $2739.81 $2226.96 $1539.63 $1777.05 $366.42 $2385.04 Label the function for the transformations of the exponential function Words to use:Vertical stretchIf negative, reflection over x-axisHorizontal shift- _ = shift _+ _ = shift _New horizontal aysmptote Vertical Stretch If negative, reflection over x-axis - c = shift right +c = shift left Horizontal Shift Vertical Shift +d = shift up - d = shift down New horizontal asymptote