Problem preview

F-IF.7.e Warmup M1-026-A03-V03

Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.

Identify the y-intercept of an exponential function

Problem

Population \(P(t)~=~500\cdot~1.06^{t}\) gives people \(t~\text{years}\) after observation begins. Verify the \(y\)-intercept by substitution, interpret it in context, and state the yearly growth rate.

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substitution = P(0)=500·1.06⁰=500; y-intercept = (0 years,500 people); meaning = observed population starts at 500 people; growth = 6% per year

intercept = (500 years,0 people); meaning = population reaches zero

P(0)=1.06·500⁰=1.06 people

growth = 106% per year; initial population 1.06

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Curriculum context

Course: Math I
Standard: F-IF.7.e
Category: Functions
Domain: Interpreting Functions
Objective: Graph exponential functions and identify intercepts and end behavior; preview logarithmic and trigonometric graph features.
Problem type: Identify the y-intercept of an exponential function