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Situational
100
Is the following growth or decay: y = 2^x and explain
It is growth because the base is a number greater than 1 and the exponent is positive
100
The population in the town of Huntersville is presently 38,300. The town grows at an exponential rate of 1.2% per year. Find the number of years it takes for the population to grow to 42,500.
What is approximately 8.7 years
100
Use y = 250e^0.12t What is the initial amount?
What is 250
100
Write an exponential growth function to model the situation. A population of 422,000 increases by 12% each year.
N(t) = 422,000e^0.12t
100
A bacteria culture doubles every 0.25 hours. At time 1.25 hours, there are 40 000 bacteria present. How many bacteria were present initially? Hint (you can create a table of values)
What is 1250
200
Is the following growth or decay: y=100*(0.5)^x
It is a decay, because the base is less than 1 and the exponent is positive
200
$1,200 is invested at an annual rate of 3.2%. Find the number of years it will take for the account balance to be twice the initial amount. Assume the interest is compounded continuously
What is approximately 21.7 years
200
Use y = 250e^0.12t What is the growth rate?
12%
200
The population of Baconburg starts off at 20,000, and grows by 13% each year. Write an exponential growth model and find the population after 10 years.
N(t) = 20,000e^0.13t and N(10)=73,386 approximately
200
How long will it take for a $2500 loan to reach 150%, if the interest on the loan is charged at 4.25% per year and compounded continuously?
Approximately 9.5 years
300
Is the following growth or decay: y= 100*(1+0.4)^t and explain
It is growth, because 1 + 0.4 = 1.4 which greater than 1 and the exponent is positive
300
The population in the town of Deersburgh is presently 30,000. The town has been growing at a steady rate of 2.7%. Find the number of years it will take for the population to grow 142 %
What is approximately 13 years
300
The function A(t) = 1200e^0.5t, models the amount of money in an account, t, years after the initial deposit. How is the interest on the investment being compounded?
continuously
300
Carolyn started an investment with $50. If the interest on her investment is compounded continuously at a rate of 11.5% each year, Write a function to model the amount in her investment after t, years
A(t) = 50e^0.115t
300
The world population doubles every 35 years. In 1980 the population was 4.5 billion. Assuming that the doubling period remains at 35 years, estimate the population in the year 2120. Hint: you can use a table of values
What is 72,000,000,000
400
Is the following growth or decay: y = 7 (1-.06)^x and explain
It is a decay, because 1 - .06 = 0.94 which is less than 1
400
Lucy started an investment with $600 compounded continuously at a rate of 8.25%. In the same year, Jordan invested $900 compounded continuously at 7.75%. Approximately, how much will be in Lucy’s account when Jordan has $1433?
approximately $984
400
y = 9.8(1.35)^t What is the growth rate? Assume the interest is compounded semiannually?
0.7 or 70%
400
Eric and Khasirr invested $700 and $1000 respectively. They agreed to withdraw their monies after 10 years to start a joint venture. If the interest on Eric’s investment is compounded monthly at a rate of 15% and Khasiir’s is compounded continuously at a rate of 12%. Write a function to model Eric's investment after t years
Eric's investment, A(t) = 700(1.0125)^12t
400
A sodium isotope, Na^24 , has a half-life of 15 hours. Determine the amount of sodium that remains from a 4 g sample after 45 hours? Hint: you may use a table of values
What is 0.5g
500
Is the following growth or decay: y = -350 (1+.25)^x and explain
it is a growth, because the base 1+ .25 = 1.25 which is greater than 1
500
A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function m(t) = 13e^(-0.015t), where m(t) is measured in kilograms When will the substance reach half its initial amount?
approximately 46 days
500
y = 9.8(1.05)^t What is the growth rate? Assume the interest is compounded quarterly
20%
500
Juma is deciding to buy a car worth $25000.The car dealer is selling it on credit at an interest rate of 6% per year for zero down payment. If a down payment of $5000 is made, the interest rate reduces to 4.5% per year. Write a function to determine how much Juma will owe the dealer ,t, years after the purchase, if she makes the down payment. Assume continuous compounded interest
What is y = 20,000e^0.045t
500
solve the equation below for t and leave your answer in exponent form ln(5t + 10) = x
t = 1/5(e^(x) - 10 )