Money Grows on Trees
An account starts with $2000 and grows 4% annually.
Write an exponential function for the value after t years.
What is y = 2000(1+0.04)^t
A bacteria culture starts with 120 cells and doubles every hour.
Write a function modeling the population after t hours.
What is y=120(2)^t ?
Rewrite the expression in simplest exponential form:
3(7)^(2x+2)
What is 147(49)^x ?
Compare the functions:
f(x)=2^x
g(x)=x^2
Which grows faster as x becomes large?
What is f(x)?
Rewrite the exponential equation in logarithmic form:
2^x=16
What is log_2(16)=x ?
An investment follows the model :
A(t)=1500(1.025)^(12t)
What annual percent growth rate does this represent?
What is 30%?
A bacteria population is modeled by
P(t) = 500(1.3)^(3t)
What does the 3 in the exponent represent in context?
Rewrite the exponential expression:
(2^3)^(x+2)
so that the x is the only term in the exponent
What is 64(8)^x ?
Compare
f(x)=0.2(5)^x
g(x)=3x+2
Which functions eventually grows faster?
What is f(x)
Solve for x:
2^x=7
Round to the nearest hundredth.
What is x = 2.81?
An account has $4000 and earns 2.4% interest compounded monthly.
Write the model and determine the balance after 10 years.
What is $5083.78?
A bacteria culture triples every 5 hours and begins with 80 bacteria.
Write the exponential model and determine the population after 15 hours.
What is y=80(3)^(t/5) ?
Simplify completely:
5(3^(2x))(3^(x+1))
What is 15(27)^x ?
Determine where the functions intersect:
2^x=16
What is x=4?
Find the inverse of
f(x)=6^x
in terms of common log.
What is
f^-1(x)=(log(x))/log(6) ?
A bank account has $3500 and earns 3.2% interest compounded annually.
How much money will be in the account after 8 years?
What is $4503.04?
A bacteria culture starts with 200 cells and grows by 18% each hour.
How many bacteria are present after 6 hours?
What is 539 cells?
Rewrite the expression so it has base 4:
(64)^(x-1)
What is (4)^(3x-3) ?
For which values of x is
4^x>2^(2x)
What is no values of x?
Evaluate:
log_2(32)
What is 5?
Two investments are offered:
Investment A: A(t)=5000(1.04)^t
Investment B: B(t) = 5000(1.02)^(2t
Which investment grows faster in the long run?
Two bacteria cultures grow according to
P(t)=200(1.5)^t
Q(t)=500(1.2)^t
Which population is larger after 10 hours?
What is the first bacteria culture?
Rewrite the expression as a single exponential expression:
4^(2x+3)*2^(x-1)
What is 2^(5x+5) ?
Determine when
3^x=50
What is x = 3.56?
Solve the equation:
3(10)^(3x)=19
Round x to the nearest thousandth.
What is x=0.267?