EXPONENTS AND EXPONENTIAL FUNCTIONS

Problem 1 :

The function f(x) = 2(2)x was replaced with f(x) + k , resulting in the function graphed below.

expo-fun-q1

What is the value of k?

Solution:

f(x) = 2(2)x

y-intercept: x = 0

y = 2(2)0

y = 2

So, the new function goes from 2 to -3. (i.e) 5 units down.

So, k = -5

Problem 2 :

Monica did an experiment to compare two methods of warming an object. The results are shown in the table below.

expo-table-q1

Which statements best describes her results?

A. The temperature using both methods changed at a constant rate.

B. The temperature using both methods changed exponentially.

C. The temperature using Method 2 changed at a constant rate.

D. The temperature using Method 2 changed exponentially.

Solution:

expo-table-s1

The temperature using Method 2 changed exponentially.

So, option (D) is correct.

Problem 3 :

The value of an antique car is modeled by the function V(x) = 107,000(1.009)(2/3x) where x is the number of years since 2005. By what approximate percent rate is the value of the car increasing per year?

A. 0.04%         B. 0.14%          C. 0.60%        D. 1.40%

Solution:

V(x)=P (1+i)nV(x)=107000 (1.009)23x=107000 (1.0060)x=107000 (1+0.006)xV(x)=107000 (1+0.6%)x

So, option (C) is correct.

Problem 4 :

Which expression is equivalent to x13-3? A. xB. 1xC.1x9D. 1x27

Solution:

= x13-3= x-33=x-1=1x

So, option (B) is correct.

Problem 5 :

Which expression is equivalent to 16x16y-2x-16y632?
A. 24x92y92B. 24x34y9C. 64x12y8D.64x12y12

Solution:

= 16x16y-2x-16y632=1632x312y-62x-312y182=64x312x312y9y3=64x612y12=64x12y12

So, option (D) is correct.

Problem 6 :

The value V, of a car can be modeled by the function V(t) = 13,000 (0.82)t, where t is the number of years since the car was purchased. To the nearest tenth of a percent, what is the monthly rate of depreciation?

A. 1.5%    B. 1.6%     C. 9.2%     D. 18.0%

Solution:

V(t) = 13,000 (0.82)t

y = a (1 - r)t

1 - r = 0.82

-r = 0.82 - 1

-r = -0.18

r = 0.18 × 100

r = 18%

So, option (D) is correct.

Problem 7 :

The current student population of the Brentwood Student Center is 2,000. The enrollment at the center increases at a rate of 4% each year. To the nearest whole number, what will the student population be closest to in 3 years?

(1) 2,240          (2) 2,250       (3) 5,488         (4) 6,240

Solution:

Given, P = total population

r = 4% = 0.04

n = 3 years

P = 2000 (1 + r)n

= 2000 (1 + 0.04)3

= 2000 (1.04)3

= 2000 (1.124864)

P = 2249.728

Rounded to the nearest whole number, and we get

P = 2250

So, option (2) is correct.

Problem 8 :

Mr. Smith invested $2,500 in a savings savings account that earns 3% interest compounded annually. He made no additional deposits or withdrawals. Which expression can be used to determine the number of dollars in this account at the end of 4 years?

(1) 2500(1 + 0.03)4             (2) 2500(1 + 0.3)4

(3) 2500(1 + 0.04)3            (4) 2500(1 + 0.4)3

Solution:

Given, P = 2500, r = 3% = 0.03, n = 1, t = 4

y=P1+rnnty=25001+0.0314y=2500(1+0.03)4

So, option (1) is correct.

Problem 9 :

Which expression is equivalent to38x2y3z4?
A. 2x32yz34B. 2x23yz43C. 2zxD. 2xz

Solution:

=38x2y3z4=813x23y33z43=2x23yz43

So, option (B) is correct.

Problem 10 :

The table below shows the average weight of a type of plankton after several weeks.

expo-fun-q10

What is the average rate of change in weight of the plankton from week 8 to week 12?

A. 0.0265 ounce per week   B. 0.0375 ounce per week

C. 0.055 ounce per week      D. 0.1125 ounce per week

Solution:

Let x = Time and y = Weight 

m=y2-y1x2-x1m=0.49-0.0412-8m=0.454m=0.1125

So, option (D) is correct.

Problem 11 :

Trina has a college fund started with a  deposit of $10,000 which earns 5% annually. If no other monies are deposited, how much money will Trina have in her fund at the end of three years?

(1) $11,500       (2) $11,576.25           (3) $15,000

(4) $25,000

Solution:

Given, P = $10000

r = 5% = 0.05

t = 3 years

y=P1+rnnty=10000 (1+0.05)3y=10000 (1.05)3y=10000 (1.157625)y=11576.25

So, option (2) is coorect.

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