Exponential functions in context (SAT) is a grade 9 math skill aligned to Common Core standard HSF.LE.A.2: construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 exponential functions in context (sat) problems our math games drill.
The function g is defined by g(t)=840(0.5)t/4. The function g models the mass, in milligrams, of a medicine in a patient's bloodstream, where t is the number of hours after an injection. According to the model, what is the estimated mass, in milligrams, of the medicine at the time of the injection?
At the time of injection, t=0. So g(0)=840(0.5)0=840 milligrams.
2
Mid-gameeasy
The function h is defined by h(t)=125(1.18)t. The function h models the number of members in a club, where t is the number of years after the club was founded. According to the model, what is the estimated number of members when the club was founded?
When the club was founded, t=0. So h(0)=125(1.18)0=125 members.
3
Mid-gameeasy
The function N is defined by N(t)=680(0.72)t/8. The function N models the number of particles detected in a radiation beam, where t is the number of millimeters the beam has traveled into a shielding material. According to the model, what is the estimated number of particles in the beam at the surface of the shielding material?
At the surface, the beam has traveled 0 millimeters, so t=0. Then N(0)=680(0.72)0=680 particles.
4
Mid-gameeasy
The function S is defined by S(t)=450(0.85)t/3. The function S models the height, in centimeters, of a snowpack, where t is the number of days after a winter storm. According to the model, what is the estimated height, in centimeters, of the snowpack 3 days after the storm?
When t=3, the exponent is 3/3=1. So S(3)=450(0.85)1=382.5 centimeters.
5
Mid-gameeasy
The function I is defined by I(t)=275(1.04)t. The function I models the balance, in thousands of dollars, of an investment account, where t is the number of months after the account was opened. According to the model, what is the estimated balance, in thousands of dollars, of the account 1 month after it was opened?
When t=1, I(1)=275(1.04)1=275⋅1.04=286 thousand dollars.
6
Mid-gameeasy
The function L is defined by L(w)=180(0.88)w/2. The function L models the light output, in lumens, from a bulb, where w is the number of weeks the bulb has been in use. According to the model, what is the estimated light output, in lumens, after 2 weeks of use?
When w=2, the exponent is 2/2=1. So L(2)=180(0.88)1=158.4 lumens.
7
Mid-gamemedium
The function D is defined by D(t)=1,500(0.6)t/5. The function D models the amount of a drug, in micrograms, in a patient's bloodstream, where t is the number of hours after a dose is given. Which statement best describes what the factor 0.6 represents in this model?
Every 5 hours, the exponent increases by 1, so the amount is multiplied by 0.6. That means 60% of the previous amount remains after each 5-hour interval.
8
Buzzer beatermedium
The function R is defined by R(t)=900(0.5)t/12. The function R models the intensity of background radiation, in millisieverts, measured t months after a person enters an underground shelter. Which statement best describes what the 12 in the expression t/12 represents?
The exponent is t/12, so when t increases by 12, the exponent increases by 1 and the intensity is multiplied by 0.5. The 12 is the number of months for one full application of the factor 0.5.
Overtime
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