1which function equation is represented by the graph?

f(x)=12(43)x

f(x)=12(32)x

f(x)=12(12)x

f(x)=12(23)x
graph on a coordinate plane with axes labeled x and f of x. an exponential curve passes through 0 comma 12, 1 comma 8, and 2 comma approximately 5.3.

2the 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

3which 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

4ramon 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

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, 12 50)}

what is the function equation in sequence notation?

enter your answer in the box.

je=

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

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction