Exponential Quiz

Pick the true statement regarding y = 5(2)^x.

• The x-intercept is (2,0).

• The asymptote is y = 2.

• The y-intercept is (0,2).

• The graph increases from left to right.

Answer explanation

2 > 1 growth = increasing

A company's stock increased exponentially for 10 years. If the stock started at $90 per share and increased 3% each year, x, which equation shows this relationship?

• y = 90(10.03)^x

• y = 10(1.03)^x

• y = 90(0.97)^x

• y = 90(1.03)^x

Answer explanation

increased = growth

y = initial value (1 + growth factor)^x

Which equation has a y-intercept of 5?

• y = 3(2)⁵

• y = 0.5(4)^x

• y = 5(3)^x

• y = 3(5)^x

Answer explanation

y = y-intercept (growth/decay factor)^x

Which equation shows the value of a rare coin doubling every year for 18 years, if the initial value of the coin was $10?

• y = 10 (18)^x

• y = 18 (10)^x

• y = 18 (2)^x

• y = 10 (2)^x

Answer explanation

y = initial value (growth pattern)^x

^{doubling = growth pattern of 2}

^{years would be x so 18 does not go in the equation}

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth

• Decay

Answer explanation

decay < 1 (but > 0; can't be negative)

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x

• y=6(1+14)^x

• y=6(1.14)^x

• y=6(0.86)^x

Jame's 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

• 70(2)³⁵

• 70(2)⁵

• 2(70)⁵

• 5(70)²

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500

• 5, 20, 80, 320

• 4, 20, 100, 500

• 4, 9, 14, 19

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x

• y = 15(1.35)^x

• y = 15(0.35)^x

• y = 35(1.15)^x

Moody's Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. Which equations shows how much will the printer be worth in x years?

• y = 35,000(0.95)^x

• y = 35,000(0.85)^x

• y = 35,000(1.95)^x

• y = 35,000(1.05)^x

Answer explanation

decay - subtract percent as a decimal from 1