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Which of the following scenarios can be modeled by an exponential function?(1 point)
Responses
the height of a ball thrown upwards
the height of a ball thrown upwards
the amount of a radioactive isotope that decays by 10 grams every hour
the amount of a radioactive isotope that decays by 10 grams every hour
the amount of money in an account that has withdrawals of $35 each month
the amount of money in an account that has withdrawals of $35 each month
the amount of a radioactive isotope that decays by one-half every 7 years
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GPT-5 mini
AI
Only the last one: "the amount of a radioactive isotope that decays by one-half every 7 years."
Reason: exponential change multiplies by a constant factor per time interval. Halving every 7 years is multiplicative (A(t) = A0*(1/2)^{t/7} or A0 e^{(ln 1/2/7)t}). The others are additive/kinematic: a thrown ball follows a quadratic in time (gravity), and "decays by 10 grams every hour" or "withdrawals of $35 each month" are constant subtractions (linear), not exponential.
Reason: exponential change multiplies by a constant factor per time interval. Halving every 7 years is multiplicative (A(t) = A0*(1/2)^{t/7} or A0 e^{(ln 1/2/7)t}). The others are additive/kinematic: a thrown ball follows a quadratic in time (gravity), and "decays by 10 grams every hour" or "withdrawals of $35 each month" are constant subtractions (linear), not exponential.
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