Functions (exponential and logarithmic)

Which of the following exponential functions represents an initial value of 1450 and a decay of 18% for x years?

Problem #14 a

MODELING REAL LIFE: A young channel catfish weighs about 0.1 pound. During the next 8 weeks, its weight increases by about 23% each week.

a. Write an exponential growth function that represents the weight of the catfish after t weeks during the 8-week period.

Mathematical Equivalence

OFF

You are depositing money into your savings account each week. After one week, you have $220. After two weeks, you have $242.

Write an exponential function modeling the scenario.

•  $f\left(x\right)=220\left(22\right)^x$ 

•  $f\left(x\right)=198\left(22\right)^x$ 

•  $f\left(x\right)=220\left(1.1\right)^x$ 

•  $f\left(x\right)=200\left(1.1\right)^x$ 

 $f\left(1\right)=7\ ;\ f\left(n\right)\ =\ 3f\left(n-1\right)$  
Which explicit equation below would describe the same set of values as the recursive equation above?

•  $f\left(n\right)\ =\ 7\times\left(3\right)^n$  

•   $f\left(n\right)=7\times\left(3\right)^{n-1}$  

•  $f\left(n\right)=3\times\left(7\right)^n$  

•  $f\left(n\right)=3\times\left(7\right)^{n-1}$  

Which of the following equations could be used to predict the value of V(t), after t years, of a 1200 dollar investment expected to appreciate by 3.5% each year?

• $1200(3.5)^t$

• $1200(1+3.5)^t$

• $1200(1+.035)^t$

• $1200(1-.35)^t$

The New York Volleyball Association invited 64 teams to compete in a tournament. After each round, half of the teams were eliminated.

Which equation represents the number of teams, t, that remained in the tournament after r rounds?

• t=64(r)^0.5

• t=64(-0.5)^r

• t=64(1.5)^r

• t=64(0.5)^r

exponential function

Layla's 4 hour daily phone time decreases by 5% per day.

• 4(1.05)^x

• 4(.5)^x

• 4(.95)^x

• 4(5)^x

Which explicit formula can be rewritten in function form as f(n) = 3/2 ⋅ 2ⁿ?

• g_n = 3/2 ⋅ 2^n-1

• g_n = 2 ⋅ 3^n-1

• g_n = 3 ⋅ 2^n-1

• g_n = 3/2 ⋅ 3^n-1

Problem #10

Write a function that represents the situation.

Your starting annual salary of $35,000 increases by 4% each year.

(a)