Answer:
Step-by-step explanation:
1. Which function equation is represented by the graph? An exponential curve passes through (0, 12), (1, 8), and (2, 5.3).
f(x)=12(43)x
f(x)=12(32)x
f(x)=12(12)x
f(x)=12(23)x
For x = 0, the functions all equal 0 at x = 0 and none of functions equal 12 at x = 0.
If you meant
f(x)=12(4/3)^x
f(x)=12(3/2)^x
f(x)=12(2/3)^x
f(x)=12(1/2)^x
For x = 0,
f(x)=12(4/3)^x = 12
f(x)=12(3/2)^x = 12
f(x)=12(2/3)^x = 12
f(x) = 12(1/2)^(0) = 12
For x = 1,
f(x)=12(4/3)^x = 16
f(x)=12(3/2)^x = 18
f(x)=12(2/3)^x = 8
f(x)=12(1/2)^(1) = 6
For x = 2,
f(x)=12(4/3)^x = 21.3
f(x)=12(3/2)^x = 27
f(x)=12(2/3)^x = 16/3 = 5.33
f(x)=12(1/2)^(2) = 3
2. The population of a city is 35,400. The population is expected to grow at a rate of 2% each year. Which function equation represents the population of the city after t years?
f(t)=35,400(1.02)^t
f(t)=35,400(2)^t
f(t)=35,400(1.2)^t
f(t)=35,400(0.02)^t
Exponential Growth Function: f(t) = P(1 + r)^t
P = 35,400
r = 2% = 2%/100 = 0.02
t = time
f(t) = 35400(1 + 0.02)^t
f(t) = 35400(1.02)^t
3. Which function equation is represented by the graph?
f(x)=40(3.25)x
f(x)=40(2.25)x
f(x)=40(1.5)x
f(x)=40(2.5)x
I don’t see a graph, but attached is each function’s graph.
4. Ramon bought a bicycle for $478. The value of the bicycle is expected to decrease at a rate of 6.5% each year. Which function equation represents the value of the bicycle after t years?
f(t)=478(1.065)^t
f(t)=478(6.5)^t
f(t)=478(0.935)^t
f(t)=478(0.065)^t
Exponential Decay Function f(t) = P(1 – r)^t
P = price = $478
r = 6.5% = 6.5% / 100 = 0.065
f(t) = 478(1 – 0.065)^t
f(t) = 35400(0.935)^t
5 The ordered pairs model an exponential function, where j is the function name and e is the input variable. {(1, 10), (2, 50), (3, 250), (4, 1250)}. What is the function equation in sequence notation?
Enter your answer in the box.
Exponential Function: y = ab^x
(1, 10); 10 = ab
(2, 50); 50 = ab^2
10 = ab
a = 10/b
50 = ab^2
a = 50/b^2
10/b = 50/b^2
b = 5
Substitute to find a with b = 5 and 10 = ab (Note, you can also substitute with 50 = ab^2):
10 = a(5)
a = 10/5
a = 2
y = (2)(5)^x
j(e) = 2(5)^e
