An 8 inch sunflower is planted in a garden and the height of...

A(n) 8-inch sunflower is planted in a garden and the height of the sunflower increases exponentially, increasing by 14% per day. Write a function f that determines the height of the sunflower (in inches) in terms of the number of days t since it was planted. f(t)= How many days after it was planted will the sunflower be 30 inches tall? days How many days after it was planted will the sunflower be 120 inches tall? days

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00:01 So recall that a general exponential function, f of t, is written as a, which is my starting or my original value times b, which is my growth or decay rate.

00:11 It's a growth rate if i'm multiplied by a value greater than one and decay if i multiply in by a value less than one.

00:17 So suppose i have a 10 -inch sunflower is planted and the height increases exponentially by 16 % per day.

00:23 So i start with 10%.

00:26 And it's growing by 16%.

00:28 So i have the original height plus my interest rate.

00:32 Oh, and excuse me, since i'm repeated multiplication leads to an exponent of t.

00:37 So i'm adding my interest rate because i need my original amount plus my interest rate.

00:42 Interest rate is always written as a decimal.

00:44 So 16 % as a decimal is 0 .16.

00:48 So 1 plus 0 .16 raise the teeth power.

00:52 And this will give me the function, f of t, is 10 times 1 .16 raised the teeth power.

01:01 How many days after it was planned will be 30 inches tall? okay, so how many days? let's say t is a day.

01:09 Right? each day it grows 16%.

01:12 So i want this equal to 30 equals 10 times 1 .16 of the teeth power.

01:20 What you do first, multiplying by 10, opposite of multiplying this dividing...

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