Exponential Functions

Exponential Functions - Growth and Decay


The population of a certain culture of bacteria at time tt is given by P(t)=P0×10ytP(t) = P_0 \times 10^{yt} , where P0P_0 is the initial amount of bacteria, yy is the growth constant, and tt is the time (in seconds). A scientist measures that the number of bacteria at time t=4t=4 is 105610^ {56} times the number of bacteria at time t=0t=0. Given this information, what is the growth constant yy of this group of bacteria?

pHpH measures the concentration of hydrogen ions H+H^+ in a solution. Let pH=mpH=m if the number of gram ions of H+H^+ in a 11-liter solution is 10m10^{-m}.

Then the ratio of the number of gram ions of H+H^+ for pH=6.5pH=6.5 and the number of gram ions of H+H^+ for pH=7.9pH=7.9 can be expressed as 10a.10^a. What is the value of 100a?100a?

The brightness of light is reduced by half when it penetrates a glass screen with 1111 cm width. If the brightness of light has been reduced to 12.5012.50 % of the initial brightness, how many glass screens with the same width did the light penetrate?

If you invest 12001200 dollars in savings account that pays 44 percent compound interest, then how long does it take to double your money? (Assume the answers are in years and the compounding occurs once a year.)

The number of particles in a given location after time tt is modeled by the equation N(t)=N0et21N(t) = N_0e^{-\frac{t}{21}}. At what time tt will the number of particles be equal to 1e3\frac{1}{e^3} of the initial number (when t=0t=0)?


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