Exponential Growth Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

medium
An investment grows from \1{,}000to to \1,5001{,}500 in 55 years with continuous compounding. Find the annual growth rate.

Solution

  1. 1
    Continuous growth: A=PertA = Pe^{rt}. So 1500=1000e5r1500 = 1000 e^{5r}, giving e5r=1.5e^{5r} = 1.5.
  2. 2
    5r=lnโก(1.5)โ‰ˆ0.40555r = \ln(1.5) \approx 0.4055, so rโ‰ˆ0.0811=8.11%r \approx 0.0811 = 8.11\%.

Answer

rโ‰ˆ8.11%r \approx 8.11\%
Continuous compounding uses A=PertA = Pe^{rt}, which is the limit of compound interest as compounding becomes infinitely frequent. To find the rate, isolate the exponential, take the natural log, and solve for rr.

About Exponential Growth

Exponential growth occurs when a quantity increases by a constant multiplicative factor over equal intervals.

Learn more about Exponential Growth โ†’

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Example 2 medium

A city's population grows at [formula] per year. If the current population is [formula], when will i

Example 4 hard

Two populations grow exponentially: [formula] and [formula]. When will [formula] overtake [formula]?

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