Exponential Growth and Decay

Benjamin invests $400 in a savings account that earns 5% percent interest each year. What is the exponential formula for this problem.

400 (1.05)^t or 400(1+.05)^t

Einsteinium-253 is an element that loses about 2/3 of its mass every month. A sample of Einsteinium-253 has 450 grams. Write a function that gives the sample's mass in grams t months from today?

450 (1-2/3)^t or 450 (1/3)^t

At the moment a hot cake is put in a cooler, the difference between the cake's and the cooler's temperatures is 50° degree Celsius. This causes the cake to cool and the temperature difference loses 1/5 of its value every minute. What's the formula?

50 (1-1/5)^t or 50 (4/5)^t

The number of bacteria in a petri dish is multiplied by a factor of 1.21 every hour. There were initially 500. What is the exponential formula for this problem?

500 (1.21)^t 0r 500 (1+.21)^t

A computer sells for $900 and loses 30% of its value per year. Write a function that gives the computer's value, V(t) t years after it is sold. (what is the formula)

900 (1-.3)^t or 900 (.70)^t

Growth or Decay? f(x)= 48 (.66)^5

Decay because .66 is a fraction between 0 and 1.

Growth or Decay? f(x)= 7.8 (.98)^5

Decay because .98 is a fraction between 0 and 1.

Growth or Decay? f(x)= 150 (1.02)^7

Growth because 1.02 is a negative or positive number greater than 1.

Growth or Decay? f(x)= 10 (1.11)^2

Growth because 1.11 is a negative or positive number greater than 1.

Growth or Decay? f(x)= 190 (1.21)^3

Growth because 1.21 is a negative or positive number greater than 1.

Sketch a graph of an exponential decay function

Left to right it appears to vanish toward a flat line

Sketch a graph of an exponential growth function.

Left to right it moves toward positive or negative infinity

N(t)= 187(1.23)^t is a function. How can you rewrite it to make it more transparent?

N(t)= 187(1 + .23)^t because 1+.23 is equal to 1.23

N(t)= 34.5(1.28)^t is a function. How can you rewrite it to make it more transparent?

N(t)= 34.5(1 + .28)^t because 1+.28 is equal to 1.28

N(t)= 86(.78)^t is a function. How can you rewrite it to make it more transparent?

N(t)= 86(1-.12)^t because 1-.12 is equal to .78

N(t)= 2187(.48)^t is a function. How can you rewrite it to make it more transparent?

N(t)=2187 (1-.52)^t because 1-.52 is .48

N(t)= 756(.67)^t is a function. How can you rewrite it to make it more transparent?

N(t)=756 (1-.33)^t because 1-.33 is .67

The expression 900 (2.25)^t gives the price performance, in bits per second per dollar, of wireless devices from a certain company as a function of years since the company began. What does 900 represent?

The company's initial price efficiency was 900 bits per second per dollar.

The expression 6.7 (1.45)^t models the number of billions of genetic sequence bases available in the public database of the Whole Genome Shotgun project t years since 2002. What does the 1.45 represent in the situation?

The number of bases in the database is multiplied by 1.45 each year.

The expression 60 (1.2)^T superscript models the number of nano-related patents granted in the US as a function of years since 1991. What does 60 represent in this expression?

There were 60 nano-related patents granted in 1991.