Writing Exponential Functions y=ab^x
In the function y=ab^x, what does the "a" represent?
original value
What does the "r" represent in the function y=a(1+/- r)^t ?
"r" represents the rate as a decimal.
Samuel has an initial amount of $50 in his bank account. Every month, he will deposit $600 in his account. Does this relation represent a linear or exponential function?
In the function y=ab^x, what does the "b" represent?
constant ratio/multiplier
When do you use the y=a(1 +/- r)^t function?
When the growth or decay rate is a percent.
A lab had an original population of 500 bacteria. Every minute, the bacteria will double. Does this relation represent a linear or exponential function?
Exponential
The number of a certain bacteria triples in a lab culture every day. Suppose there are 100 bacteria to start an experiment. Write a function for the number of bacteria, f(x) as a function of the number of days, x.
f(x)=100(3)^x
The initial value of a painting is worth $54,000 and is increasing at a rate of 6% each year. Write an exponential function that represents this situation.
y=54000(1 + 0.06)^t
Farah has $500 in her savings account. She is looking at two investment plans. Under plan A, she will increase her account balance by $65 a year. Under plan B, she will increase her account balance by 18% each year. Write a function to represent plan A.
y = 500 + 65x
A radioactive substance has an initial mass of 100 grams and its mass is reduced by half every year. Write a function to represent the number of grams, f(t), remaining after t years.
f(t) = 100(1/2)^t
The initial value of a painting is worth $54,000 and is increasing at a rate of 6% each year. What will the value of the painting be in 8 years?
$86,067.80
Farah has $500 in her savings account. She is looking at two investment plans. Under plan A, she will increase her account balance by $65 a year. Under plan B, she will increase her account balance by 18% each year. Write a function to represent plan B.
y = 500 (1+ 0.18)^t
If a population of 250 bacteria quadruples every hour, write a function that represents p(t), the population after t hours?
p(t) = 250(4)^t
A population of gorillas in an area is 15,000 and is decreasing at a rate of 13% per year. At this rate, what will the approximate gorilla population be in 7 years?
5658 gorillas
Farah has $500 in her savings account. She is looking at two investment plans. Under plan A, she will increase her account balance by $65 a year. Under plan B, she will increase her account balance by 18% each year. Approximately how much more will she save with plan B after 5 years?
$318.88