Writing Exponential given points
Write the equation of an exponential function with an initial value of 2 and goes through the point (1,4)
N(x) = 2(2)x
Image 1
y = 1(2)x
When using the function A(t) = aert, how would you write r if I told you it was 12.5%?
0.125
f(x) = 2(3)x What is f(2)
18
We invest $2000 in a retirement account with 3% interest compounded annually. How much will we have in 20 years?
A(t) = P(1+r/n)nt
$3612.22
Write the equation of an exponential that goes through the points (0,2) and (1,3)
N(x) = 2(3/2)x
Image 2
If you have an investment of $10, earing 10% per year compounded continuously, how much would you have after 1 year?
About $11.05
Is f(x) = 2(-3)x an exponential function? Why or why not?
No, b cannot be negative or 1
We invest 1000 dollars in an account that has 5.5% APR compounding quarterly. How much will the account have in 25 years?
$3918.2
Write the equation of an exponential that goes through the points (0,4) and (2,1)
N(x) = 4(1/2)x
Image 3
N(x) = -3(3)x
If you had an investment of $2000 earning 23% per year compounding continuously, how much would you have after 3 years?
About $3987.43
Population of a group of seals started at 6. Their groups is growing at a rate of 19% per year. After 20 years, how many seals will there be/ (assuming none die). f(x) = 6(1.19)x
Roughly 194 or 195 seals
If you want to buy a car in 4 years that costs $3500, how much should you invest in an account that has 1.5% APR compounded monthly?
$3296.299
Write the equation of an exponential that goes through (0,2) and (3,1).
N(x) = 2(0.79)x
Image 4
N(x) = 1(2.45)x
If a mineral decays at a continuous rate of 4% per day, how much will 500g of the mineral decay to in 7 days?
About 377.89 grams
Population of otters was 13 in 2000. The population has an annual growth rate of 2%. What will the population be in 2010? 13(1.02)x
about 15 or 16 otters
You want to put a down payment on an apartment in 8 years which would cost $20,000. If you invest now in an account that has 3% APR compounding daily, how much would you need to invest?
$15732.712
Write the equation of an exponential that goes through (1,2) and (3,6)
N(x) = (1.15)(1.732)x
Image 5
N(x) = 2(1.8)x
A mineral decays at a continuous rate of 12.3% per day. How much will 5000g decay to in 2 weeks?
About 893.54 grams
Population of apes was 30 in 2012. The annual growth rate is 4%. How many apes would be present in 2030, assuming none die?
About 60 or 61 apes
In 40 years you would like to retire with $100,000. If you invest $5,000 in an account that compounds quarterly, what is the smallest APR your account can have? To the nearest hundredth.
Approximately 0.0756 which is roughly 7.6%.