Finding
Growth Factors
Growth Factors
Does the equation y=3(1.02)^x represent growth or decay? How do you know?
(For an extra 100 points: what percent is it growing or decaying by?
It is growing because the growth factor (1.02) is greater than 1.
1.02 represents 102%, so we are growing by 2%
Rewrite the equation 3^2 = 9 in log form.
log_(3)9=2
Rewrite the equation log_(6)216 = 3 in exponential form.
6^3=216
WITHOUT using the calculator, calculate
log_(7)49
The answer is 2 because
7^2=49
A box of granola bars currently sells for $4.29.
Write an equation for the cost of the box in x years if the price increases (from inflation) by 2% a year.
y=4.29(1.02)^x
Does the equation y=5(0.94)^x represent growth or decay? How do you know?
(For an extra 100 points: what percent is it growing or decaying by?
It is decaying because the growth factor (0.94) is less than 1.
0.94 represents 94%, so we are decaying by 6%
Rewrite the equation 7^3 = 16807 in log form.
log_(7)16807=3
Rewrite the equation log_(5)625 = 4 in exponential form.
5^4=625
WITH the calculator, calculate log_9 4782969
The answer is 7 because
9^7 = 4782969
A new Macbook that costs $1,295 brand new loses value at a rate of about 19% a year.
Write an equation for the value of the Macbook, x years after purchase.
y=1295(0.81)^x
What is the growth factor that represents 5% growth?
1.05
Rewrite the equation 1.02^x = 5 in log form.
log_(1.02)5=x
Rewrite the equation log_(1.01)2 = x in exponential form.
1.01^x=2
Solve the equation 1.03^x=2 using logs. Show all work.
1.03^x=2
log_(1.03)2=x
23.45=x
The value of a Macbook x years after purchase can be represented by the equation y=1295(0.81)^x
What is the approximate value of the Macbook after 3 years?
y=1295(0.81)^3
y=688.22 dollars
What is the growth factor that represents 14% decay?
0.86
Rewrite the equation 0.76^x = 0.32 in log form.
log_(0.76)0.32=x
Rewrite the equation log_(0.98)0.73 = x in exponential form.
0.98^x=0.73
Solve the equation 7=2(1.5)^x using logs. Show all work.
7=2(1.5)^x
3.5=1.5^x
log_(1.5)3.5=x
3.09=x
The value of a Macbook x years after purchase can be represented by the equation y=1295(0.81)^x
How many years will it take for the Macbook to be worth only $100? Show all work.
100=1295(0.81)^x
0.077=0.81^x
log_(0.81)0.077=x
12.17=x
What is the growth factor that represents 9.8% growth?
1.098
Rewrite the equation 1.16^4 = y in log form.
log_(1.16)y=4
Rewrite the equation log_(1.048)y = 12 in exponential form.
1.048^12=y
Solve the equation 4=10(0.9)^x using logs. Show all work.
4=10(0.9)^x
0.4=0.9^x
log_(0.9)0.4=x
8.7=x
The cost of a box of granola bars in x years can be found with the equation y=4.29(1.02)^x
How many years will it take for the box to cost $6.50?
6.50=4.29(1.02)^x
1.515=1.02^x
log_(1.02)1.515=x
20.98=x